Limits, Continuity & Differentiability · Evaluation of limits

Let

\lim_{x\to2}\dfrac{\left(\tan(x-2)\right)\left(rx^2 + (p-2)x - 2p\right)}{(x-2)^2} = 5

for some

r, p \in \mathbb{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.

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