Quadratic Equation And Inequalities

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