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. \[\cos\left( \frac{1}{3} \cos^{-1} p \right)\] \[\cos\left( \frac{4}{3} \cos^{-1} p \right)\] \[\frac{\pi}{2}-\cos\left( 3 \cos^{-1} p \right)\] \[\cos\left( 3 cos^{-1} p \right)\]