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प्रश्न
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.
विकल्प
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.
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उत्तर
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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