Question

Let $f\left(x\right)=a{x}^2+bx+c,a,b,c\in R$. If $f\left(x\right)$ takes real values for real values of $x$ and non-real values for non-real values of $x$, then

• A. $a=0$
• B. $b=0$
• C. $c=0$
• D. Nothing can be said about $a,b,c$

Answer 1

The correct option is A $a=0$

$f\left(x\right)$ takes real values for real values of $x$ non real values for non real values of $x$

If 2nd degree term exists in the question for non real multiple of $i$cancels with rest of the equation and gives us the real term

Here the only condition is 2nd degree coefficient must be zero

$\therefore a=0$