If for some p, q, r ∈ R, not all have same sign, one of the roots of the equation ( p^2+ q^2) x^2-2 q ( p + r ) x+ q^2+ r^2=0 is also a root of the…

If for some p, q, r $\displaystyle \in \mathbf{R}$, not all have same sign, one of the roots of the equation $\displaystyle \left(\mathrm{p}^2+\mathrm{q}^2\right) x^2-2 \mathrm{q}(\mathrm{p}+\mathrm{r}) x+\mathrm{q}^2+\mathrm{r}^2=0$ is also a root of the equation $\displaystyle x^2+2 x-8=0$, then $\displaystyle \frac{\mathrm{q}^2+\mathrm{r}^2}{\mathrm{p}^2}$ is equal to \_\_\_\_.