Question

Determine whether `x = (-1)/3` and `x = 2/3` are the solutions of the equation 9x² – 3x – 2 = 0.

Answer 1

Given,

⇒ 9x² – 3x – 2 = 0

⇒ 9x² – 6x + 3x – 2 = 0

⇒ 3x(3x – 2) + 1(3x – 2) = 0

⇒ (3x + 1)(3x – 2) = 0

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

⇒ 3x = –1 or 3x = 2

⇒ `x = (-1)/3` or `x = 2/3`

Hence, `(-1)/3, 2/3` are the solutions of the equation 9x² – 3x – 2 = 0.