FACTORIZATION | SOLVE QUADRATIC EQUATIONS BY FACTORIZATION | 10th CLASS MATHEMATICS

SOLUTION OF QUADRATIC EQUATIONS BY FACTORIZATION EXPLAINED WITH EXAMPLES IN URDU/HINDI 10^TH CLASS MATHEMATICS

·         SOLUTION OF QUADRATIC EQUATIONS BY FACTORIZATION:

In this method here are the few steps to follow:

i)                    Write the quadratic equation in the standard form as

ax² + bx + c = 0

ii)                  Now multiply ‘a’ and ‘c’ as ‘ac’.

iii)                Factorize the obtained product ‘ac’.

iv)                Take a pair of those digits from factorization of ‘ac’ which add ups to form ‘bx’ and multiply to form ‘ac’.

v)                  Take commons from the obtained equation.

vi)                Again take commons and keep possibly one relation equal to zero.

vii)              Two possibilities of variable to keep equal to zero.

viii)            Keep those relations twice equal to zero and find values of variable ‘x’.

·         Example: Solve the quadratic equation by factorization.

                  3x² – 6x = x + 20

The standard form of equation is   3x² – 7x – 20 = 0

Here a = 3, b = -7, c = -20              and ‘ac’ = 3 x (-20) = -60

Possible pairs of -60 are; -30 x 2 , -15 x 4 , -12 x 5 , -10 x 6 , -20 x 3 which if multiply give -60 

Nothing of these pairs by combining form -7x but the pair -12x + 5x.

Therefore the equation can be written as

                                                      3x² -12x + 5x -20 = 0

Taking common as,                                   3x (x – 4) + 5 (x – 4) = 0

Again taking common;                   (x – 4) (3x + 5) = 0

Now there are two possibilities, either x – 4 = 0 or 3x + 5 = 0 because both are multiples of each other.

If  x – 4 = 0          then     x = 4

And if        3x + 5 = 0        then     3x = -5             &         x = -5/3

Therefore the roots of quadratic equation 3x² – 7x -20 = 0 are ‘-5’ and ‘-5/3’.

The solution set is {-5, -5/3}.

For understanding more comprehensively, watch the video from start to end and full procedure of factoring the Quadratic Equation has been explained with many examples.

Here is the video lecture explaining quadratic equations in Urdu/Hindi in the most easy and efficient way. In this video, you'll get to know a brief note on solution of Quadratic Equations by Factorization in Urdu/Hindi. You'll be able to know how to solve Quadratic Equations by Factorization? And the full procedure of solving Quadratic Equations by Factorization step by step. Also you'll get to know the complete process of solving Quadratic Equations with much type of examples. If there's any confusion regarding this video lecture, you can comment or contact us directly through social links provided so your comments will e entertained gladly. Get everything related to study and academic content through this blog and youtube channel for useful and important notes and materials.

Thanks for visiting blog, also visit my youtube channel for more informative and useful videos and lectures. 

Read More

INTRODUCTION TO QUADRATIC EQUATIONS | 10th CLASS MATHEMATICS

Introduction to Quadratic Equations in Urdu/Hindi Chapter 1/ 10th Class Mathematics 

• QUADRATIC EQUATIONS

• Definition:- An equation which contains the square of unknown (variable) but no higher power is called a Quadratic Equation or an Equation of Second Degree.

• Standard Form:- If we have a variable ‘x’ the standard form of a quadratic equation is

                                               

ax² + bx + c = 0          a≠0      ……………… (A)

In the above equation, a, b & c are some real numbers. ‘a’ is called coefficient of ‘x²’ , ‘b’ is called coefficient of ‘x’ and ‘c’ is called a constant.

In equation (A), it is given that ‘a’ must not be equal to zero. If we take a = 0, then the equation will be no longer a quadratic equation but a linear equation. So it is necessary to mention that ‘a’ must not be equal to zero. Although a may have negative value as well as positive value.

If a = 0, then               

(0)x² + bx + c = 0

                                    0     +   bx + c = 0

                                                bx + c = 0        (A linear equation)

So,       6x² + 4x - 3 = 0 & -3x² + 5x + 2 = 0 are two quadratic equations. Also x² + 9x = 20 is a quadratic equation but not in the standard form.

• Pure Quadratic Equation:- In a quadratic equation, if we put b = 0, then the equation reduces as

                                   

ax² + (0)x + c = 0

                                    ax² +    0   + c = 0

                                               ax²  + c = 0       (A pure quadratic equation)

Thus, 3x² + 9 = 0 & 5x² = 30 are pure quadratic equations.

• From the all above mentioned equations, we can find out the constants a, b & c by comparing these equations with the standard form equation (A).

• Variable:- A variable is allotted for some specific numeric value and is unknown or changeable. As from its name, it is oriented from the word ‘vary’ which means ‘change’. So variable means ‘changeable.’ It has no fixed or constant value, with time those values may change. Just for instance, if we have a variable ‘x’ in an equation, it may have some specific value but we cannot say that this value is specified to ‘x’ forever. It has some value in this equation and may have some different value in the other. Therefore, a variable does not have a fixed numeric value.
• Constant:- On the other hand, a constant is specified for a fixed numeric value. Its value does not change with the passage of time. For example, '5' is five today and will be '5' tomorrow. It'll not change its value with time. Also the speed of light is represented by 'c' and c = 3x10⁸ms^-1.  Thus this 'c' is a constant having constant value which would never be changed anywhere and anytime. Therefore, a constant has a fixed numeric value.

Here is the video lecture explaining quadratic equations in Urdu/Hindi in the most easy and efficient way. In this video you'll get to know a brief introduction of Quadratic Equations in Urdu/Hindi. You'll be able to know what the quadratic equations actually are and how to recognize these equations? Which parameters are used in quadratic equations? What are necessary conditions for equations to be quadratic ones? What is the standard form of quadratic equations? Here's all you get in this lecture. Get everything related to study and academic content through this channel and blog for useful and important notes and materials.

 Thanks for visiting blog, also visit my youtube channel for more informative and useful videos and lectures. 

Read More