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Mathematics — CBSE Class 10 board question

Q1. [1]
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.
  1. A Both Assertion (A) and Reason (R) are true; and Reason (R) is the correct explanation of Assertion (A).
  2. B Both Assertion (A) and Reason (R) are true; but Reason (R) is not the correct explanation of Assertion (A).
  3. C Assertion (A) is true but Reason (R) is false.
  4. D Assertion (A) is false but Reason (R) is true.
Previously asked in CBSE board exam
2023 30/6/1 Q19
Generated by claude-sonnet-4-6 · 2026-06-15 10:32 · grounding rag
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?

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