Question

Let \( \lim_{x \to 2} \frac{\tan(x - 2)\,[r x^2 + (p - 2)x - 2p]}{(x - 2)^2} = 5 \) for some \( r, p \in \mathbb{R} \). If the set of all possible values of \( q \), such that the roots of the equation \( r x^2 - p x + q = 0 \) lie in \( (0, 2) \), be the interval \( (\alpha, \beta] \), then \( 4(\alpha + \beta) \) is equal to:

• A. 11
• B. 21
• C. 17
• D. 13

Hint:

When roots lie in \((d, e)\), always check four conditions: Discriminant, the value of the function at the boundaries, and the position of the vertex.

Answer 1

The Correct Option is C