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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 co-efficients occur in conjugate pairs.
Options
Both Assertion (A) and Reason (R) are true; and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true; but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.
Solution
Both Assertion (A) and Reason (R) are true; and Reason (R) is the correct explanation of Assertion (A).
Explanation:
Sum of roots = `5 + sqrt(7) + 5 - sqrt(7)` = 10,
which is a rational number.
and product of roots = `(5 + sqrt(7)) (5 - sqrt(7))`
= 25 – 7
= 18
which is also a rational number.
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