Solve the quadratic equation 8x² - 14x + 3 = 0

(i) When x ∈ I (integers)

(ii) When x ∈ Q (rational numbers)

Given,

⇒ 8x² - 14x + 3 = 0

⇒ 8x² - 12x - 2x + 3 = 0

⇒ 4x(2x - 3) - 1(2x - 3) = 0

⇒ (4x - 1)(2x - 3) = 0

⇒ 4x - 1 = 0 or 2x - 3 = 0

⇒ 4x = 1 or 2x = 3

⇒ x = $\dfrac{1}{4}$ or x = $\dfrac{3}{2}$.

(i) Since, there is no integer in the solution,

Hence, no solution.

(ii) Here, x ∈ Q

Hence, x = $\dfrac{1}{4}, \dfrac{3}{2}$.