Question

Solve the following equation by factorisation method:

`2/3 x^2-1/3 x-1 = 0, x\cancel=0`

Answer 1

Given:

`2/3 x^2-1/3 x-1 = 0, x\cancel=0`

Multiply the whole equation by 3:

2x² − x − 3 = 0

a = 2, b = −1, c = −3

a × c

= −6

We need two numbers whose product = −6 and sum = −1.

These numbers are 2 and −3.

2x² + 2x − 3x − 3 = 0

(2x² + 2x) − (3x + 3) = 0

2x(x + 1) − 3(x + 1) = 0

(x + 1) (2x − 3) = 0

x + 1 = 0

⇒ x = −1

2x − 3 = 0

⇒ x = `3/2`

x = −1 or x = `3/2`