Question

Let \( f(x) = x^{2} + ax + b \), where \( a, b \in \mathbb{R} \). If \( f(x)=0 \) has all its roots imaginary, then the roots of \( f(x) + f'(x) + f''(x) = 0 \) are

• A. real and distinct
• B. imaginary
• C. equal
• D. rational and equal

Hint:

If a quadratic $f(x)$ has no real roots, then the sum of $f(x)$ and its derivatives also has no real roots.

Answer 1

The Correct Option is B