Solve the following equation by factorization:

5x² - 12x - 9 = 0, when (i) x ∈ I (ii) x ∈ Q

Given,

⇒ 5x² - 12x - 9 = 0

⇒ 5x² - 15x + 3x - 9 = 0

⇒ 5x(x - 3) + 3(x - 3) = 0

⇒ (5x + 3)(x - 3) = 0

⇒ (5x + 3) = 0 or (x - 3) = 0      [Using Zero-product rule]

⇒ 5x = -3 or x = 3

⇒ x = $\dfrac{-3}{5}$ or x = 3.

(i) Since, x ∈ I

Hence, x = {3}.

(ii) Since, x ∈ Q

Hence, x = $\Big{3, \dfrac{-3}{5}\Big}$.