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.
