Friday, 31 December 2021

Age of industrialization

Before the Industrial Revolution
Proto-industrialisation is referred to the phase which existed even before factories began in England and Europe. There was large-scale industrial production for an international market not based on factories. In the seventeenth and eighteenth centuries, merchants from Europe moved to the countryside, supplying money to peasants and artisans, requesting them to produce for an international market. Merchants were restricted to expand their production within towns because rulers granted different guilds the monopoly right to produce and trade in specific products. In the countryside, poor peasants and artisans eagerly agreed so that they could remain in the countryside and continue to cultivate their small plots. The Proto-industrial system was thus part of a network of commercial exchanges controlled by merchants.

The Coming Up of the Factory
In the 1730s the earliest factories in England were set up, but only in the late eighteenth century, the number of factories multiplied. Cotton was the first symbol of the new era and its production boomed in the late nineteenth century. Richard Arkwright created the cotton mill where costly machines were set up and all the processes were brought together under one roof and management.

The Pace of Industrial Change
First: In Britain, the most dynamic industries were cotton and metals. Cotton was the leading sector in the first phase of industrialisation up to the 1840s, followed by iron and steel industry. Second: The new industries found it difficult to displace traditional industries. Third: The pace of change in the ‘traditional’ industries was not set by steam-powered cotton or metal industries, but they did not remain entirely stagnant either. Fourth: technological changes occurred slowly.

James Watt improved the steam engine produced by Newcomen and patented the new engine in 1781. His industrialist friend Mathew Boulton manufactured the new model. Steam engines were not used in any of the other industries until much later in the century.

Hand Labour and Steam Power
There was no shortage of human labour in Victorian Britain. Industrialists had no problem of labour shortage or high wage costs. Instead of machines industrialists required large capital investment. The demand for labour was seasonal in many industries. In all such industries where production fluctuated with the season, industrialists usually preferred hand labour, employing workers for the season.

Life of the Workers
The workers’ lives were affected by the abundance of labour in the market. To get a job, workers should have existing networks of friendship and kin relations in a factory. Till the mid-nineteenth century, it was difficult for workers to find jobs. In the early nineteenth century, wages were increased. The fear of unemployment made workers hostile to the introduction of new technology. Spinning Jenny was introduced in the woollen industry. After the 1840s, building activity intensified in the cities, opening up greater opportunities for employment. Roads were widened, new railway stations came up, railway lines were extended, tunnels dug, drainage and sewers laid, rivers embanked.

The Age of Indian Textiles
In India, silk and cotton goods dominated the international market in textiles, before the age of machine industries. A variety of Indian merchants and bankers were involved in this network of export trade – financing production, carrying goods and supplying exporters. By the 1750s this network, controlled by Indian merchants, was breaking down. The European companies came into power – first securing a variety of concessions from local courts, then the monopoly rights to trade. The shift from the old ports to the new ones was an indicator of the growth of colonial power. European companies controlled trade through the new ports and were carried in European ships. Many old trading houses collapsed, and those who wanted to survive had to operate within a network shaped by European trading companies.

Weaver and Manchester
After the 1760s, the consolidation of the East India Company did not initially lead to a decline in textile exports from India. Before establishing political power in Bengal and Carnatic in the 1760s and 1770s, the East India Company had found it difficult to ensure a regular supply of goods for export. After the East India Company established political power, it developed a system of management and control that would eliminate competition, control costs, and ensure regular supplies of cotton and silk goods. It was established by following a series of steps.

By eliminating existing traders and brokers connected with the cloth trade, and establishing more direct control over the weaver.
By preventing Company weavers from dealing with other buyers.
The weavers were granted a loan to buy the raw materials once an order was placed. Weavers who took loans needed to hand over the cloth they produced to the gomastha. Weaving required the labour of the entire family, with children and women all engaged in different stages of the process. Earlier, supply merchants had a very close relationship with weavers, but new gomasthas were outsiders with no social link with the village.

In many places in Carnatic and Bengal, weavers set up looms in other villages where they had some family relation. In other places, weavers along with the village traders revolted, opposing the Company and its officials. Over time many weavers began refusing loans, closing down their workshops and taking to agricultural labour. By the turn of the nineteenth century, cotton weavers faced a new set of problems.

Manchester Comes to India
In 1772, Henry Patullo said that the demand for Indian textiles could never reduce since no other nation produced goods of the same quality. But, unfortunately, by the beginning of the nineteenth century, India witnessed a decline in textile exports. In the early nineteenth century, exports of British cotton goods increased dramatically. At the end of the eighteenth century, import of cotton piece-goods was restricted into India. In India cotton weavers faced two problems:

Their export market collapsed
Local market shrank and glutted with Manchester imports.
By the 1860s, weavers faced a new problem. They could not get sufficient supply of raw cotton of good quality. Even the raw cotton exports from India increased due to which the price increased. By the end of the nineteenth century, other craftspeople faced yet another problem. Factories in India began production, flooding the market with machine-goods.

Factories Come Up
In 1854, the first cotton mill in Bombay set up and went into production two years later. By 1862 four more mills were set up and around the same time jute mills came up in Bengal. The first jute mill was set up in 1855 and another one after seven years in 1862. In the 1860s, in north India, the Elgin Mill was started in Kanpur, and a year later the first cotton mill of Ahmedabad was set up. By 1874, the first spinning and weaving mill of Madras began production.

made his fortune in the China trade. In Bombay, Parsis like Dinshaw Petit and Jamsetjee Nusserwanjee Tata built huge industrial empires in India. Seth Hukumchand, a Marwari businessman set up the first Indian jute mill in Calcutta in 1917. The opportunities of investments in industries opened up and many of them set up factories.

But due to colonial power, Indians were barred from trading with Europe in manufactured goods and had to export mostly raw materials and food grains – raw cotton, opium, wheat and indigo – required by the British. Three of the biggest European Managing Agencies are Bird Heiglers & Co., Andrew Yule, and Jardine Skinner & Co. who mobilised capital, set up joint-stock companies and managed them.

Where Did the Workers Come From?
As the factories started expanding, the demand for workers increased. Most of the workers came from the neighbouring districts in search of work. Over 50 per cent workers in the Bombay cotton industries in 1911 came from the neighbouring district of Ratnagiri, while the mills of Kanpur got most of their textile hands from the villages within the district of Kanpur. As news of
employment spread, workers travelled great distances in the hope of work in the mills.

Even after the demand for workers increased, getting jobs was difficult. The numbers seeking work were always more than the jobs available. Most of the industrialists employed a jobber, which he brought from his village, to recruit new workers. Industrialists helped the jobber to settle down and provided them with money in need.

The Peculiarities of Industrial Growth
European Managing Agencies were interested in certain kinds of products such as tea and coffee. They established tea and coffee plantations and invested in mining, indigo and jute. These products are used only for export purposes. In the late nineteenth century, Indian businessmen began setting up industries. The yarn produced in Indian spinning mills was used by handloom weavers in India or exported to China. The pattern of industrialisation was affected by a series of changes. When the swadeshi movement gained support, nationalists boycotted foreign cloth. From 1906, Indian yarn exports to China declined since produce from Chinese and Japanese mills flooded the Chinese market. Till the end of the First World War, industrial growth was slow. The war completely changed the whole scenario and Indian mills took advantage of the situation. They had a vast market to supply war needs: jute bags, cloth for army uniforms, tents and leather boots, horse and mule saddles and a host of other items. The industrial production boomed over the years and after the war, Manchester could never recapture its old position in the Indian market.

Small-scale Industries Predominate
Small-scale industries continued to predominate the rest of the country. Only a small proportion of the total industrial labour force worked in registered factories. The rest worked in small workshops and household units. Handicrafts production expanded in the twentieth century. In the twentieth century, handloom cloth production expanded. It happened because of technological changes as they started adopting new technology which helped them improve production without excessively pushing up costs.

Certain groups of weavers were in a better position than others to survive the competition with mill industries. Some of the weavers produced coarse cloth while others wove finer varieties. Weavers and other craftspeople who continued to expand production through the twentieth century did not necessarily prosper. They worked for long hours including all the women and children. But they were not simply remnants of past times in the age of factories. Their life and labour were integral to the process of industrialisation.

Market for Goods
When new products are produced advertisements helped people to make products appear desirable and necessary. They tried to shape the minds of people and create new needs. Today we are surrounded by advertisements which appear in newspapers, magazines, hoardings, street walls, television screens. From the very beginning of the industrial age, advertisements played a part in expanding the markets for products, and in shaping new consumer culture.

Manchester industrialists put labels on the cloth bundles, to mark the quality. When buyers saw ‘MADE IN MANCHESTER’ written in bold on the label, they were expected to feel confident about buying the cloth. 
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Tuesday, 28 December 2021

★How do organism reproduce ★

 8: How Do Organisms Reproduce
Introduction
*Reproduction
Reproduction is the process by which all organisms multiply in number and increase their population.
Asexual reproduction
Asexual reproduction is a method of reproduction that involves only one organism. A single organism reproduces two or multiple organisms on its own. This is seen in all unicellular organisms, some multicellular organisms and a few plants.
Sexual reproduction
The mode of reproduction that involves two individuals; one male and one female. They produce sex cells or gametes which fuse to form a new organism.

Asexual Reproduction
1.Fission
Fission is an asexual reproduction that is common in most of the unicellular organisms.
When the fission results in two daughter cells, it is binary fission (e.g. paramecium).
When fission results in many daughter cells, it is called multiple fission (e.g. Plasmodium).
Planes of fission may be different for different organisms.

2.Budding
Budding is a type of asexual reproduction in which a small cyst-like structure is formed on the parent’s body, which gives rise to a new individual.
Bud may remain attached to the parent (yeast) or may separate and become a new individual (hydra).
3..Regeneration and fragmentation
Regeneration is the process of growing back the lost organ or body part by the organism (e.g. lizard).
Fragmentation is the process by which an organism gets fragmented into smaller pieces and each piece grows into a whole new organism.
E.g. Planaria, Hydra
4.Spore formation
Organisms such as fungi make spores that can grow into complete new individuals when dispersed from their fruiting body.
5.Vegetative propagation
This is a type of asexual reproduction seen in plants.
The vegetative part of the plant, like leaves, stem, roots, gives rise to a new plant.
Vegetative propagation can be artificial or natural.
Natural vegetative propagation happens through leaves (e.g. bryophyllum), stem (e.g. turmeric, ginger), runners/stolon (e.g.grass runners, strawberry), bulbs ( e.g. onion, lily), etc.
Artificial methods include cutting, grafting, layering and plant tissue culture.

Sexual Reproduction
Types of Cell division
Two types of cell division seen in eukaryotic organisms:

1.Mitosis
Takes place in somatic cells
Maintains the chromosome number
Produces two, diploid daughter cells
Required for asexual reproduction, development and growth, cell replacement and regeneration

2.Mieosis
Takes place in sex cells
Reduces the number of chromosomes by half
Produces four haploid daughter cells
Required for sexual reproduction, i.e gamete formation
To know more about Cell division, subscribe my channel on YouTube ๐Ÿ‘‰click here

The Reproductive System
To know more about Human Reproductive System, visit here.

1.Male reproductive system
The main reproductive organ in males is a pair of testes.
They produce the male sex cells called sperms and also produce male sex hormone testosterone.
★Male main reproductive organs
The main reproductive organ in males is a pair of testes.
They are present in scrotal sacs outside the body and contain seminiferous tubules as the structural and functional unit.
Male sex cells, sperms, are produced by seminiferous tubules and mature in the epididymis.
Leydig cells or interstitial cells present in between the seminiferous tubules secrete hormone testosterone.
Male accessory reproductive organs
Several accessory reproductive organs that aid in the reproductive process.
The prostate gland and the seminal vesicles are glands of reproductive system which make semen and nourish the sperms.
Penis, having urethra passing through it, is called copulatory organ.
Male Ducts
In males, the vas deferens and the urethra are the main ducts.
A single vas deferens carries sperms from respective testis up to urethra.
Urethra acts as a common passage for semen and urine.
2.Female reproductive system
The human female reproductive system consists of a pair of ovaries, a pair of fallopian tubes/oviducts and the accessory organs such as the uterus and the vagina.
★Female main reproductive organ
The main reproductive organ in a female is a pair of ovaries.
They produce the female sex cells called eggs or ova and also produce female sex hormones called estrogen and progesterone.
Female accessory reproductive organ
Uterus and vagina are the accessory reproductive organs in human females.
The uterus is the site of fetal development and vagina receives sperms from the male.
★Menstrual Cycle
Menstruation
Menstruation is the cyclic event of the release of the ovum from the ovary and its removal from the body when fertilization does not happen.
During menstruation, the blood-rich endometrium of the uterus also breaks down while the ovum is being removed from the body.
Two pituitary hormones, LH and FSH and two ovarian hormones, estrogen and progesterone, all have their roles in menstruation.
In humans, the cycle repeats every 28 days.
๐ŸงFertilization
Human reproduction
Humans reproduce sexually. The male produces sperms and the female produces eggs. When the sperm fuses with the egg, it forms a zygote that gives rise to a new progeny.
★ some important method to preserve pregnancy
1.Contraceptive Methods
Reproductive health
Reproductive health deals with the prevention of STDs and unwanted pregnancy. Understanding the reproductive system is also a part of reproductive health awareness.

Contraceptives
Contraceptives are devices that prevent unwanted pregnancy and help avoid STDs.
Contraceptives can be of various types such as mechanical barriers, hormonal/chemical methods, surgical methods, etc.
Coitus Interruptus
It is a very unreliable contraceptive method where the coitus is stopped before the male ejaculates inside the female reproductive tracts.
Rhythm Method
Another unreliable method of contraception where coitus is avoided when the female is fertile and the chances of fertilization are very high.
Condoms
One of the most effective methods of contraception.
A mechanical barrier that stops the semen from entering the female tract preventing pregnancy.
It also avoids the possibility of contracting STDs.
Diaphragms
Diaphragms are barriers that can be added inside the female reproductive tracts.
They stop the entry of semen inside the female tract and thus prevent pregnancy.
Contraceptive Pills
Contraceptive pills are chemical methods of contraception.
They change the level of hormones in the body that prevents the release of the ovum from the ovaries.
Emergency Pill
Emergency pills are those pills which can be taken after coitus to avoid pregnancy.
They quickly change the level of hormones in the body and prevent a successful implantation even if the egg gets fertilized.
IUD
IUD stands for Intrauterine Device.
They can be used for a couple of years.
It is a device that is inserted into the uterus, changing its shape and preventing successful implantation of the zygote.
Sterilization
Sterilization is a surgical method of going permanently sterile.
This can be done in both males and females.
In males, it is called vasectomy and in females, it is called tubal ligation.
To know more about Contraceptive Methods, visit here.

Reproduction in Plants
1.Sexual reproduction in flowering plants
Sexual reproduction in plants happens through flowers.
Essential whorls of the flowers such as androecium and the gynoecium help in the sexual reproduction of plants.
Non-essential parts of flowers
The typical structure of flower contains essential whorls and non-essential whorls.
Sepals and Petals are called non-essential whorls as they do not directly take part in reproduction.
Sepals protect the inner delicate whorl during bud condition and also perform photosynthesis if they are green in colour.
Petals, when they are coloured, attract insects for pollination.
Essential whorls of flowers
Androecium and gynoecium are called as essential/reproductive whorls of a flower.
Androecium produces pollen grains containing male gametes and gynoecium produces ovules which are female gametes.
Bisexual flowers contain both the whorls while unisexual flowers contain either of them.
Each individual member of androecium is called a stamen and consists of anther and filament.
Anther produces haploid pollen grains.
Each individual member of gynoecium is called pistil and consists of stigma, style and ovary.
Pollination
The process of transfer of pollen grains from anthers to the stigma of a flower is known as pollination.
It is required for fertilization.
Pollination has two types, self-pollination (autogamy) and cross-pollination (allogamy).
In self-pollination, transfer of pollen grains takes place from anthers to the stigma of the same flower or another flower of the same plant.
In cross-pollination, pollens are transferred from anthers to the stigma of another flower.
Many pollinating agents play their roles in cross-pollination. Examples: water, wind, insects, birds, bats, etc.
Fertilization
Fusion of male and female gametes is known as fertilization.
In flowering plants after pollination, the pollens germinate on the stigma surface of pistil and generate two male nuclei.
Ovule has egg cell and two polar nuclei.
One male nucleus fuses with two polar nuclei and forms triploid endosperm.
Another male nucleus fuses with the egg cell and forms the zygote that gives rise to the embryo and future plant.
After fertilization, ovary becomes fruit and ovules turn into seeds. All other parts wither away.

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Thursday, 23 December 2021

money and credit class 10th

Welcome to Hamid learning zone
Study Material and Notes of Ch 3

Money and Credit Class 10th


Economics

Topics in the Chapter
 • Overview 
• Money as a medium of exchange
• Modern form of money
 • Loon activities of bank 
• Two difforont cracit situation
 • Terms of credit 
• Formal sector credit in indlic

• Solf-holp groups for the poor

Overview

Money as a Medium of Exchange

Money acts as an intermediate in the exchange process, it is called a medium of exchange. A person holding money can easily exchange it for any commodity or service that he or she might want.

Modern form of Money

In the early ages, Indians used grains and cattle as money. Thereafter came the use of metallic coins – gold, silver, copper coins – a phase which continued well into the last century. Now, the modern forms of money include currency – paper notes and coins. The modern forms of money – currency and deposits – are closely linked to the workings of the modern banking system.

Currency

In India, the Reserve Bank of India issues currency notes on behalf of the central government. No other individual or organisation is allowed to issue currency. The rupee is widely accepted as a medium of exchange in India.

Deposits in Banks


The other form in which people hold money is as deposits with banks. People deposit their extra cash with the banks by opening a bank account in their name. Banks accept the deposits and also pay an amount as interest on the deposits.

The deposits in the bank accounts can be withdrawn on demand, these deposits are called demand deposits. The payments are made by cheques instead of cash.

A cheque is a paper instructing the bank to pay a specific amount from the person’s account to the person in whose name the cheque has been issued.

Loan Activities of Banks

Banks keep only a small  proportion of their deposits as cash with themselves. These days banks in India hold about 15% of their deposits as cash. This is kept as a provision to pay the depositors who might come to withdraw money from the bank on any given day. Banks use the major portion of the deposits to extend loans. There is a huge demand for loans for various economic activities. Banks charge a higher interest rate on loans than what they offer on deposits. The difference between what is charged from borrowers and what is paid to depositors is their main source of income for banks.

Two Different Credit Situations

Credit (loan) refers to an agreement in which the lender supplies the borrower with money, goods or services in return for the promise of future payment.

Here are 2 examples which help you to understand how credit works.

Festive Season:
In this case, Salim obtains credit to meet the working capital needs of production. The credit helps him to meet the ongoing expenses of production, complete production on time, and thereby increase his earnings. In this situation, credit helps to increase earnings and therefore the person is better off than before.

Swapna’s Problem:
In Swapna’s case, the failure of the crop made loan repayment impossible. She had to sell part of the land to repay the loan. Credit, instead of helping Swapna improve her earnings, left her worse off. This is an example of debt-trap. Credit, in this case, pushes the borrower into a situation from which recovery is very painful. Whether credit would be useful or not, depends on the risks in the situation and whether there is some support, in case of loss.

Terms of Credit

Every loan agreement specifies an interest rate which the borrower must pay to the lender along with the repayment of the principal. In addition, lenders also demand collateral (security) against loans.

Collateral (Security) is an asset that the borrower owns (such as land, building, vehicle, livestocks, deposits with banks) and uses this as a guarantee to a lender until the loan is repaid. If the borrower fails to repay the loan, the lender has the right to sell the asset or collateral to obtain payment.

Interest rate, collateral and documentation requirement and the mode of repayment, together is called the terms of credit. It may vary depending on the nature of the lender and the borrower.

Formal Sector Credit in India
Cheap and affordable credit is crucial for the country’s development. The various types of loans can be grouped as:

Formal sector loans:

These are the loans from banks and cooperatives. The Reserve Bank of India supervises the functioning of formal sources of loans. Banks have to submit information to the RBI on how much they are lending, to whom, at what interest rate, etc.

Informal sector loans:

These are the loans from moneylenders, traders, employers, relatives and friends, etc. There is no organisation which supervises the credit activities of lenders in the informal sector. There is no one to stop them from using unfair means to get their money back.

Formal and Informal Credit

The formal sector meets only about half of the total credit needs of rural people. The remaining credit needs are met from informal sources. It is important that the formal credit is distributed more equally so that the poor can benefit from the cheaper loans.

It is necessary that banks and cooperatives increase their lending, particularly in rural areas, so that the dependence on informal sources of credit reduces.
While the formal sector loans need to expand, it is also necessary that everyone receives these loans.

Self Help Groups for the Poor

Poor households are still dependent on informal sources of credit because of the following reasons:

Banks are not present everywhere in rural India.
Even if banks are present, getting a loan from a bank is much more difficult as it requires proper documents and collateral.
To overcome these problems, people created Self Help Groups (SHGs). SHGs are small groups of poor people which promote small savings among their members. A typical SHG has 15-20 members, usually belonging to one neighbourhood, who meet and save regularly.

Advantages of Self Help Group (SHG)
It helps borrowers to overcome the problem of lack of collateral.
People can get timely loans for a variety of purposes and at a reasonable interest rate.
SHGs are the building blocks of organisation of the rural poor.
It helps women to become financially self-reliant.
The regular meetings of the group provide a platform to discuss and act on a variety of social issues such as health, nutrition, domestic violence, etc.
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We hope “CBSE Notes Class 10 Economics Chapter 3 – Money and Credit” helped you in your studies. Keep Learning and stay tuned for more updates on CBSE and NCERT. 

Sunday, 19 December 2021

Quadratic Equation

Welcome to Hamid learning zone we are going to discuss Quadratic Equation
All we know that what is quadratic polynomial.
Yes lets study points by points.

Quadratic polynomial:- a polynomial having degree 2. Std.form:- ax²+bx+c        p(x)= ax²+bx+c

Quadratic Equation:- Equation of quadratic polynomial  i.e.
ax²+bx+c =0is a quadratic polynomial.
Solving QE by Factorisation
Roots of a Quadratic equation
The values of x for which a quadratic equation is satisfied are called the roots of the quadratic equation.

If ฮฑ is a root of the quadratic equation ax2+bx+c=0, then aฮฑ2+bฮฑ+c=0.

A quadratic equation can have two distinct real roots, two equal roots or real roots may not exist.

Graphically, the roots of a quadratic equation are the points where the graph of the quadratic polynomial cuts the x-axis.

Consider the graph of a quadratic equation x2−4



Graph of a Quadratic Equation
In the above figure, -2 and 2 are the roots of the quadratic equation x2−4=0
Note:

If the graph of the quadratic polynomial cuts the x-axis at two distinct points, then it has real and distinct roots.
If the graph of the quadratic polynomial touches the x-axis, then it has real and equal roots.
If the graph of the quadratic polynomial does not cut or touch the x-axis then it does not have any real roots.
Solving a Quadratic Equation by Factorization method
Consider a quadratic equation 2x2−5x+3=0
⇒2x2−2x−3x+3=0
This step is splitting the middle term
We split the middle term by finding two numbers (-2 and -3) such that their sum is equal to the coefficient of x and their product is equal to the product of the coefficient of x2 and the constant.
(-2) + (-3) = (-5)
And (-2) × (-3) = 6
2x2−2x−3x+3=0
2x(x−1)−3(x−1)=0
(x−1)(2x−3)=0
In this step, we have expressed the quadratic polynomial as a product of its factors.
Thus, x = 1 and x =3/2 are the roots of the given quadratic equation.
This method of solving a quadratic equation is called the factorisation method.

For More Information On Solving a Quadratic Equation by Factorization method, Watch this video

Solving QE by Completing the Square
Solving a Quadratic Equation by Completion of squares method
Ye topic removed hai phir bhi jise dekhna h dekh lo
In the method of completing the squares, the quadratic equation is expressed in the form (x±k)2=p2.

Consider the quadratic equation 2x2−8x=10
(i) Express the quadratic equation in standard form.
2x2−8x−10=0

(ii) Divide the equation by the coefficient of x2 to make the coefficient of x2 equal to 1.
x2−4x−5=0

(iii) Add the square of half of the coefficient of x to both sides of the equation to get an expression of the form x2±2kx+k2.
(x2−4x+4)−5=0+4

(iv) Isolate the above expression, (x±k)2 on the LHS to obtain an equation of the form (x±k)2=p2
(x−2)2=9

(v) Take the positive and negative square roots.
x−2=±3

x=−1 or x=5

To know more about Solving Quadratic Equations by Completing the Square, visit here.

Solving QE Using Quadratic Formula
Quadratic Formula
Quadratic Formula is used to directly obtain the roots of a quadratic equation from the standard form of the equation.

For the quadratic equation ax2+bx+c=0,

x= [-b± √(b2-4ac)]/2a

By substituting the values of a,b and c, we can directly get the roots of the equation.

To know more about Quadratic Formula, visit here.

Discriminant
For a quadratic equation of the form ax2+bx+c=0, the expression b2−4ac is called the discriminant, (denoted by D), of the quadratic equation.
The discriminant determines the nature of roots of the quadratic equation based on the coefficients of the quadratic equation.

For More Information On Discriminant, Watch The Below Video.

Solving using Quadratic Formula when D>0

Solve 2x2−7x+3=0 using the quadratic formula.
(i) Identify the coefficients of the quadratic equation. a = 2,b = -7,c = 3
(ii) Calculate the discriminant, b2−4ac
D=(−7)2−4×2×3= 49-24 = 25
D> 0, therefore, the roots are distinct.
(iii) Substitute the coefficients in the quadratic formula to find the roots

x= [-(-7)± √((-7)2-4(2)(3))]/2(2)

x=(7 ±5)/4

x=3 and x= 1/2 are the roots.

Nature of Roots

Based on the value of the discriminant, D=b2−4ac, the roots of a quadratic equation can be of three types.

Case 1: If D>0, the equation has two distinct real roots.

Case 2: If D=0, the equation has two equal real roots.

Case 3: If D<0, the equation has no real roots.

For More Information On Nature Of Roots, Watch The Below Videos.

Be More Curious
Graphical Representation of a Quadratic Equation
The graph of a quadratic polynomial is a parabola. The roots of a quadratic equation are the points where the parabola cuts the x-axis i.e. the points where the value of the quadratic polynomial is zero.

Now, the graph of x2+5x+6=0 is:

In the above figure, -2 and -3 are the roots of the quadratic equation
x2+5x+6=0.

For a quadratic polynomial ax2+bx+c,

If a>0, the parabola opens upwards.
If a<0, the parabola opens downwards.
If a = 0, the polynomial will become a first-degree polynomial and its graph is linear.

The discriminant, D=b2−4ac
Nature of graph for different values of D.
If D>0, the parabola cuts the x-axis at exactly two distinct points. The roots are distinct. This case is shown in the above figure in a, where the quadratic polynomial cuts the x-axis at two distinct points.

If D=0, the parabola just touches the x-axis at one point and the rest of the parabola lies above or below the x-axis. In this case, the roots are equal.
This case is shown in the above figure in b, where the quadratic polynomial touches the x-axis at only one point.

If D<0, the parabola lies entirely above or below the x-axis and there is no point of contact with the x-axis. In this case, there are no real roots.
This case is shown in the above figure in c, where the quadratic polynomial neither cuts nor touches the x-axis.

Formation of a quadratic equation from its roots
To find out the standard form of a quadratic equation when the roots are given:
Let ฮฑ and ฮฒ be the roots of the quadratic equation ax2+bx+c=0. Then,
(x−ฮฑ)(x−ฮฒ)=0
On expanding, we get,
x2−(ฮฑ+ฮฒ)x+ฮฑฮฒ=0, which is the standard form of the quadratic equation. Here, a=1,b=−(ฮฑ+ฮฒ) and c=ฮฑฮฒ.

Sum and Product of Roots of a Quadratic equation
Let ฮฑ and ฮฒ be the roots of the quadratic equation ax2+bx+c=0. Then,
Sum of roots =ฮฑ+ฮฒ=-b/a
Product of roots =ฮฑฮฒ= c/a

 

For More Information On Sum and Product of Roots of a Quadratic equation, Watch The Below Video

Practice Questions on Quadratic Equations Class 10
1. Check whether the following are quadratic equations:
(i) (x – 2)2 + 1 = 2x – 3
(ii) x(x + 1) + 8 = (x + 2) (x – 2)
(iii) x (2x + 3) = x 2 + 1
(iv) (x + 2)3 = x 3 – 4
2. Find two numbers whose sum is 27 and product is 182.
3. Find the roots of 4x2 + 3x + 5 = 0 by the method of completing the square.
4. Find the roots of the quadratic equation 3x2 – 5x + 2 = 0, if they exist, using the quadratic formula.
5. Find the values of k for which the quadratic equation kx(x – 2) + 6 = 0 has two equal roots.

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Friday, 17 December 2021

Wake up for term 2

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Thursday, 16 December 2021

Heredity and Evolution notes pdf

 Heredity and Evolution

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CBSE Notes Class 10 Geography Chapter 6 - Manufacturing Industries Production of goods in large quantities after processing from raw materia...