Question

Assertion (A): If one root of the quadratic equation 4x² – 10x + (k – 4) = 0 is reciprocal of the other, then value of k is 8.

Reason (R): Roots of the quadratic equation x² – x + 1 = 0 are real.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) gives the correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) does not give 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

Assertion (A) is true but Reason (R) is false.

Explanation:

Assertion: We have,

4x² – 10x + (k – 4) = 0

Product of zeroes = 1

So, `("k" - 4)/4` = 1

k = 8

Assertion is correct.

Reason: For quadratic equation, x² – x + 1 = 0

We have, Discriminant = (–1)² – 4 = –3 < 0

So, no real roots are possible.

Reason is incorrect.

Hence, Assertion is correct and reason is incorrect.