**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 quadrati

Question

**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 coefficients occur in conjugate pairs.

Accepted Answer

Step 1: Both A and R are true. Surd roots of quadratic equations with rational coefficients occur in conjugate pairs, which directly explains why the other root is $5 - \sqrt{7}$.

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Solution