Question

If $f\left(x\right)=a{x}^2+bx+c$ has no real zeroes and $a+b+c<0$, then

• A. c=0
• B. c > 0
• C. c < 0
• D. $c\ge 0$

Answer 1

The correct option is C c < 0

The graph of the function satisfying the given conditions is shown in the above picture.

We can observe that the graph doesn't touch the X-axis i.e. it doesn't have any real roots and the value of $f\left(1\right)=a+b+c<0$.

Now substitue $x=0$.

Then we can observe that $f\left(0\right)=c<0$

$\therefore$ Option C is corrrect.