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.

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