Question

Assertion (A): The discriminant of the quadratic equation $$x^{2} + 2 \sqrt{2}x + 1 = 0$$ is greater than zero.

Reason (R): If the discriminant of a quadratic equation is greater than zero, the quadratic equation has real and distinct roots.

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

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

Explanation:

Step 1 – Assertion: A is true. Here, $$a = 1$$, $$b = 2\sqrt{2}$$ and $$c = 1$$. $$D = b^{2} - 4ac = (2\sqrt{2})^{2} - 4 \times 1 \times 1 = 8 - 4 = 4 > 0$$. Therefore, the discriminant is greater than zero.

Step 2 – Reason: R is true. If $$D > 0$$, the roots are real and distinct.

Step 3 – Link: Since the discriminant is greater than zero, the roots are real and distinct; therefore, R correctly explains A.