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

1. $\dfrac{1}{2}$

2. $\dfrac{-1}{2}$

3. $\dfrac{2}{3}$

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

⇒ $x = -\dfrac{1}{2}$ or x = $\dfrac{2}{3}$.

Hence, $-\dfrac{1}{2}, \dfrac{2}{3}$ are the solutions of equation 6x² - x - 2 = 0.