Let lim_x → 2 (( tan (x-2))( r x^2+( p -2) x-2 p ))/((x-2)^2)=5 for some r, p ∈ R. If the set of all possible values of q, such that the roots of the…

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