Question

Find which of the following are the solutions of the equation 6x² – x – 2 = 0?

(i) `1/2`

(ii) `(-1)/2`

(iii) `2/3`

Answer 1

Given,

⇒ 6x² – x – 2 = 0

⇒ 6x² – 4x + 3x – 2 = 0

⇒ 2x(3x – 2) + 1(3x – 2) = 0

⇒ (2x + 1)(3x – 2) = 0

⇒ 2x + 1 = 0 or 3x – 2 = 0   ...[Using Zero-product rule]

⇒ 2x = –1 or 3x = 2

⇒ `x = -1/2` or `x = 2/3`

Hence, `-1/2, 2/3` are the solutions of equation 6x² – x – 2 = 0.