Question

The graph of a quadratic polynomial $y={px}^2-qx+r$ is as shown in the adjacent figure, then

• A. $r^2-4q<0$
• B. $r^2-4p<0$
• C. $p+q>0$
• D. $r-p-q>0$

Answer 1

Answer: (A)

$r^2-4q<0$

Here graph is

$y=p{x}^2-qx+r$

From graph, we inter that

$p<0$ $\to$ downward slope

Also product of roots $<0$

$\therefore \frac{r}{p}<0$

$\therefore r>0$

$\therefore$ Also sum of roots $>0$

$\therefore \frac{-(-q)}{p}>0$

$\therefore \frac{q}{p}>0$

$\therefore q<0$

$\therefore r^2-4q<0$.