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.

Answer 1

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.