Question

The graph of the quadratic polynomial ; $y=a{x}^2+bx+c$ is as shown in the figure. Then

• A. $b^2-4ac>0$
• B. $b>0$
• C. $a<0$
• D. All of these

Answer 1

The correct option is D All of these

Clearly we see that the quadratic equation has 2 real roots

$\therefore b^2-4ac>0$

And vertex of parabola lies in fourth quadrant $\to$x is positive and y is negative

Coordinates of vertex of parabola =$(\frac{-b}{2a},\frac{4ac-b^2}{4a})$

As y is negative $\Rightarrow \frac{4ac-b^2}{4a}<0$

$\Rightarrow a>0$ as $\frac{4ac-b^2}{4a}<0$

And x coordinate is positive $\Rightarrow \frac{-b}{2a}>0$

$\therefore b<0$

Final answer is: $b^2-4ac>0,b<0,a>0$