Question

If the set of values of $p$ for which roots of the equation $2 x^2-(2 p-3) x+2=0$ are $2^{\frac{-2}{\sin ^{-1} \alpha}}$ and $2^{\frac{2}{\pi} \sin ^{-1} \alpha}$ for some value of $\alpha$ in $[-1,1]$ is $[a, b]$, then $12(a+b)$ is

• A. 30
• B. 50
• C. 90
• D. 100

Answer 1

Answer: (C)

For any value of $\alpha$, product of the roots is 1 and sum of the roots lying in $\left[2, \frac{5}{2}\right]$
$\therefore 2 \leq \frac{2 p -3}{2} \leq \frac{5}{2} \Rightarrow 4 \leq 2 p -3 \leq 5 \Rightarrow p \in\left[\frac{7}{2}, 4\right]$