IITJEE problem

Geometry Level 4

Let $-1 \leq p \leq 1$ , find the sum of all the roots of $4x^3-3x-p=0$ lying in the interval $[\frac{1}{2},1]$ .

None of the given.

\cos\left( \frac{1}{3} \cos^{-1} p \right)

\cos\left( \frac{4}{3} \cos^{-1} p \right)

\cos\left( 3 cos^{-1} p \right)

\frac{\pi}{2}-\cos\left( 3 \cos^{-1} p \right)