Limit, Continuity and Differentiability: JEE Main 2026 Mathematics question

Let $\displaystyle\lim_{x\to2}\frac{(\tan(x-2))(rx^2+(p-2)x-2p)}{(x-2)^2}=5$ for some $r, p\in\mathbf{R}$. If the set of all possible values of $q$, such that the roots of the equation $rx^2-px+q=0$ lie in $(0,2)$, be the interval $(\alpha,\beta]$, then $4(\alpha+\beta)$ equals :