Question

Assertion (A): The roots of the quadratic equation $$3x^{2} + 7x + 8 = 0$$ are imaginary.

Reason (R): The discriminant of a quadratic equation is always positive.

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 true, but R is false.

Explanation:

Step 1 – Assertion: A is true. For the given equation, $$a = 3$$, $$b = 7$$ and $$c = 8$$. $$D = b^{2} - 4ac = 7^{2} - 4 \times 3 \times 8 = 49 - 96 = -47 < 0$$. A negative discriminant means the roots are unequal and imaginary.

Step 2 – Reason: R is false. The discriminant is not always positive; it can be positive, zero or negative. Here, it is $$-47$$.