In question numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose…

Question

In question numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option.
Statement A (Assertion): If $5 + \sqrt{7}$ is a root of a quadratic equation with rational co-efficients, then its other root is $5 - \sqrt{7}$.
Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.

Accepted Answer

## Model Answer **Option A** — Both Assertion (A) and Reason (R) are true; and Reason (R) is the correct explanation of Assertion (A). Since surd roots of a quadratic equation with rational coefficients occur in conjugate pairs, if $5+\sqrt{7}$ is a root, then $5-\sqrt{7}$ must be the other root. ## Explanation The key principle (Reason) is that irrational/surd roots always appear in conjugate pairs when coefficients are rational. This directly explains why the Assertion is true — making R the correct explanation of A. Always check: does R *explain* A, or just happen to be true alongside it?

Mathematics — Standard (041) — CBSE Class 10 board question