Question

If $g\left(x\right)=a{x}^2+bx+c$ is the given graph and a,b and c are constants, and if $abc\ne 0$, then

• A. $ac>1$
• B. $c>1$
• C. $ac>0$
• D. $a>0$

Answer 1

The correct option is C $ac>0$

Since it is a downward parabola, $a<0$. Also, the $y_{intercept}$ is less than 0. Hence $g\left(0\right)<0$ or $c<0$. Now both the roots are greater than 0, hence their sum is also greater than 0. Therefore $\frac{-b}{a}>0$ or $\frac{b}{a}<0$. But $a<0$, Hence $b>0$.

Therefore, $a<0$, $c<0$ and $b>0$.