If $\mathrm{a}(\mathrm{p}+\mathrm{q}{)}^2+2\mathrm{bpq}+\mathrm{c}=0\text{ and }\mathrm{a}(\mathrm{p}+\mathrm{r}{)}^2+2\mathrm{bpr}+\mathrm{c}=0,(\mathrm{a}\ne 0),$then 

Given,$\mathrm{a}(\mathrm{p}+\mathrm{q}{)}^2+2\mathrm{bpq}+\mathrm{c}=0\text{ and }\mathrm{a}(\mathrm{p}+\mathrm{r}{)}^2+2\mathrm{bpr}+\mathrm{c}=0$
$\begin{array}{l}\Rightarrow \mathrm{q}\text{ and }\mathrm{r}\text{ satisfy the equation }\mathrm{a}(\mathrm{p}+\mathrm{x}{)}^2+2\mathrm{bpx}+\mathrm{c}=0\\ \Rightarrow \mathrm{q}\text{ and }\mathrm{r}\text{ are the roots of }\end{array}$
${\mathrm{ax}}^2+2(\mathrm{ap}+\mathrm{bp})\mathrm{x}+\mathrm{c}+{\mathrm{ap}}^2=0$
$\Rightarrow \mathrm{qr}=\text{ Product of roots }=\frac{\mathrm{c}+{\mathrm{ap}}^2}{\mathrm{a}}={\mathrm{p}}^2+\frac{\mathrm{c}}{\mathrm{a}}$