Question

Assertion :If $a^2+b^2+c^2<0$, then if roots of the equation $a{x}^2+bx+c=0$ are imaginary, then they are not complex conjugates. Reason: Equation $a{x}^2+bx+c=0$ has complex conjugate roots when a, b, c are real.

• 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 A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

The roots of a quadratic equation are complex conjugates ($p+iq,p-iq$) only if the coefficients, i.e. a, b, c are real.
If $a^2+b^2+c^2<0$, it implies that at least one of a, b, c are imaginary (since minimum value of a perfect square of a real number is zero).
Since one of a, b, c are imaginary, the roots of the quadratic will not be complex conjugates of one another.
Hence, (A) is correct.