Quadratic Equation And Inequalities

Let $\mathop {\lim }\limits_{x \to 2} \frac{(\tan (x-2))\left(\mathrm{r} x^2+(\mathrm{p}-2) x-2 \mathrm{p}\right)}{(x-2)^2}=5$ for some $\mathrm{r}, \mathrm{p} \in \boldsymbol{R}$. If the set of all possible values of q , such that the roots of the equation $\mathrm{r} x^2-\mathrm{p} x+\mathrm{q}=0$ lie in $(0,2)$, be the interval $(\alpha, \beta]$, then $4(\alpha+\beta)$ equals :