Question

If $a{x}^2+bx+c<0,\forall x\in R$, then $a^2{x}^2+abx+ac$ is

• A. always positive
• B. always negative
• C. equal to zero
• D. can be positive or negative

Answer 1

The correct option is A always positive

Given, $a{x}^2+bx+c<0,\forall x\in R$
So, $a<0$ and $D<0$
Hence, $a^2{x}^2+abx+ac$
$=a(a{x}^2+bx+c)>0$