Question

Assertion (A): If one root of the quadratic equation $$4x^{2}-10x+(k-4)=0$$ is the reciprocal of the other then the value of $$k$$ is 8.

Reason (R): The roots of the quadratic equation $$x^{2}-x+1=0$$ are real.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

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

Explanation:

Step 1 – Assertion: A is true. The product of the roots is $$\frac{k-4}{4}.$$ If the roots are reciprocals, their product is 1; hence $$\frac{k-4}{4}=1,$$ giving $$k=8.$$

Step 2 – Reason: R is false. The discriminant of $$x^{2}-x+1=0$$ is $$(-1)^{2}-4(1)(1)=-3<0,$$ so its roots are not real.