Question

If $a{x}^2+bx+c=0$ has no real roots and $a+b+c<0$, then

• A. $c<0$
• B. $c=0$
• C. $c>0$
• D. Can't say anything

Answer 1

The correct option is A

$c<0$

$f\left(x\right)=a{x}^2+bx+c$

$f\left(1\right)=a+b+c<0$

Given that $f\left(x\right)=0$ has no real roots, so, we can say that $f\left(x\right)<0$ for all $x$.

$\therefore f\left(0\right)<0\Rightarrow c<0$