# 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.