Question

lf $x\in R$ and the roots of $a{x}^2+bx+c=0$ are non-real complex, then the sign of $a^2{x}^2+abx+ac$ is

• A. always positive
• B. always negative
• C. always non-negative
• D. always zero

Answer 1

Answer: (A)

always positive

The equation $a{x}^2+bx+c=0$ has no real roots .
$\Rightarrow b^2-4ac<0$
Consider the expression, $a^2{x}^2+abx+ac$
Here, $\Delta =a^2(b^2-4ac)<0$
and the coefficient of $x^2>0$ .
So, this expression $>0$ .