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.

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