Solve the equation by factorization method.

Given:

To find: Roots of the equation

Method Used:

To solve the quadratic equation by factorisation method, follow the steps:

1) Multiply the coefficient of x² and constant term.

2) factorise the result obtained in step 1.

3) Now choose the pair of factors in such a way that after adding or subtracting(splitting) them

You get coefficient of x.

Explanation:

Consider ,

Apply the formula:

(a + b)² = a² + b² + 2ab

(a - b)² = a² + b² - 2ab

a²-b² = (a-b) (a +b)

Cross multiply the terms to get,

⇒ 7(-12) = 48(x² – 9)

⇒ -84x = 48x² – 432

⇒ 4x² + 7x – 36 = 0

⇒ 4x² + 16x – 9x – 36 = 0

⇒ 4x (x + 4) -9(x + 4) = 0

⇒ (4x – 9) (x + 4) = 0

Hence the roots are .