If , where , has a unique root in , then the root…

MATHEMATICS · Single correct · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

If 4x3−3x−p=04x^3-3x-p=0, where −1≤p≤1-1\le p\le1, has a unique root in [12,1]\left[\frac12,1\right], then the root is (1) cos⁡−1p3\frac{\cos^{-1}p}{3} (2) cos⁡(13cos⁡−1p)\cos\left(\frac{1}{3}\cos^{-1}p\right) (3) cos⁡(cos⁡−1p)\cos(\cos^{-1}p) (4) None of these

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