Question

Assertion :If $a>0$ and $b^2-ac<0$, then domain of the function $f\left(x\right)=\sqrt{a{x}^2+2bc+c}$ is R. Reason: If $b^2-ac<0$, then $a{x}^2+2bc+c=0$ has imaginary roots.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

In Assertion, as $a>0$ and discriminant of equation greater than $0$, quantity under square root is always positive.The graph of equation is always above the x-axis. So domain of $f\left(x\right)$ is $R$.

Reason is correct as discriminant is less than $0$, quadratic equation will have imaginary roots, but it is not correct explanation for assertion.