Assertion (A): The roots of the quadratic equation 8x² + 2x - 3 = 0 are -$\dfrac{1}{2}$ and $\dfrac{3}{4}$.

Reason (R): The roots of the quadratic equation ax² + bx + c = 0 are given by $x = \dfrac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$.

1. Both A and R are true, and R is the correct explanation of A.

2. Both A and R are true, but R is not the correct explanation of A.

3. A is true, but R is false.

4. A is false, but R is true.

Given,

⇒ 8x² + 2x - 3 = 0

Comparing equation 8x² + 2x - 3 = 0 with ax² + bx + c = 0, we get :

a = 8, b = 2 and c = -3.

By formula,

x = $\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Substituting values we get :

$\Rightarrow x = \dfrac{-(2) \pm \sqrt{(2)^2 - 4 \times (8) \times (-3)}}{2 \times (8)} \\[1em] = \dfrac{-2 \pm \sqrt{4 + 96}}{16} \\[1em] = \dfrac{-2 \pm \sqrt{100}}{16} \\[1em] = \dfrac{-2 \pm 10}{16} \\[1em] = \dfrac{-2 + 10}{16} \text{ or } \dfrac{-2 - 10}{16} \\[1em] = \dfrac{8}{16} \text{ or } \dfrac{-12}{16} \\[1em] = \dfrac{1}{2} \text{ or } \dfrac{-3}{4}.$

Thus, A is false, R is true.

Hence, option 4 is the correct option.