Question

If $a,b,c\in R$ and the quadratic equation $a{x}^2+bx+c=0$ has no real roots, then

• A. $a+b+c<0$
• B. $c<0$
• C. $a+b+c>0$
• D. $(a+b+c)c>0$

Answer 1

The correct option is D $(a+b+c)c>0$

Either the graph lies above the curve or below the curve as there are no real roots $f\left(1\right)f\left(0\right)>0⟹(a+b+c)c>0$ others can't be judged because we don't know about nature of $a$.