Question

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

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

Options

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

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

• A is true, but R is false.

• A is false, but R is true.

Answer 1

A is false, but R is true.

Explanation:

Step 1 – Assertion: A is false. For the equation, $$a = 8$$, $$b = 2$$ and $$c = -3$$. $$D = 2^{2} - 4 \times 8 \times (-3) = 4 + 96 = 100$$ $$x = \frac{-2 \pm \sqrt{100}}{16} = \frac{-2 \pm 10}{16}$$. Thus, the roots are $$\frac{1}{2}$$ and $$-\frac{3}{4}$$, not $$-\frac{1}{2}$$ and $$\frac{3}{4}$$.

Step 2 – Reason: R is true. The roots of the quadratic equation $$ax^{2} + bx + c = 0$$ are given by $$x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$$.