Question

The given figure shows the graph of $f\left(x\right)=a{x}^2+bx+c$, then

• A. $ac<0$
• B. $bc>0$
• C. $ab>0$
• D. $abc<0$

Answer 1

Answer: (A), (B), (D)

$ac<0$
$abc<0$
$bc>0$

From the graph, we can conclude :
1. The parabola is opening downward. Hence coefficient of $x^2$ is negative.
So, $a<0$.
2. One of the roots is positive while the other root is negative.
Hence the product of the roots is negative.
$\Rightarrow \frac{c}{a}<0$
Since $a$ is negative, $c>0$
3. The magnitude of the positive root is greater than the magnitude of the negative root. Hence, the sum of the roots must be greater than zero.
Hence $\frac{-b}{a}>0$.
Hence, $b>0$.
Hence, options A,B and D are correct.