Question

If 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)

The correct options are
A $ac<0$
B $bc>0$
D $abc<0$

Since the curve is opening downwards so $a<0$

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

$f\left(0\right)=a(0{)}^2+b(0)+c=c,$

$f\left(0\right)>0$ as shown in graph so $c>0$

So $ac<0$

Let $\alpha$ and $\beta$ be the root

Let $\alpha <0$ and $\beta >0$

From the graph $\alpha <\beta$

Positive root is greater in magnitude than negative so

$\alpha +\beta =\frac{-b}{a}$

and from graph $\alpha +\beta >0$

So $\frac{-b}{a}>0$ and as $a<0$

so $b>0$

so $abc<0$

and $bc>0$