Solve Quadratic Equation by Factorisation

Here you will learn how to solve quadratic equation by factorisation with examples.

Let’s begin –

Solve Quadratic Equation by Factorisation

Step 1. Splitting of middle term :

(i) If the product of a and c = +ac

then we have to choose two factors ac whose sum is equal to b.

(ii) If the product of a and c = -ac

then we have to choose two factors of ac whose difference is equal to b.

Step 2 : Let the factors of $ax^2 + bx + c$ be (dx + e) and (fx + g)

$\implies$ (dx + e) (fx + g) = 0

Either  dx + e =  or  fx + g = 0 

$\implies$  x = -$e\over d$   or   x = -$g\over f$

Example : Solve the equation : $2x^2 – 11x + 12$ = 0.

Solution : We have, $2x^2 – 11x + 12$ = 0

$2x^2 – 8x – 3x + 12$ = 0

2x (x – 4) – 3 (x – 4) = 0

(x – 4) (2x – 3) = 0

$\implies$  x – 4 = 0   or   2x – 4 = 0

$\implies$  x = 4   or   x  = $3\over 2$

Hence, x = 4 and x = $3\over 2$  are the roots of the given equation.

Example : Solve the equation : $3x^2 – 14x – 5$ = 0.

Solution : We have, $3x^2 – 14x – 5$ = 0

$3x^2 – 15x + x – 5$ = 0

3x (x – 5) + 1 (x – 5) = 0

(x – 5) (3x + 1) = 0

$\implies$  x – 5 = 0   or   3x + 1 = 0

$\implies$  x = 5   or   x  = -$1\over 3$

Hence, x = 5 and x = -$1\over 3$  are the roots of the given equation.