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Question: If 0 ≤ φ ≤ 3π , then the set of all value of φ for which sum of the squares of the roots of the equa...

If 0 ≤ φ ≤ 3π , then the set of all value of φ for which sum of the squares of the roots of the equation x2 + (sin φ – 1) x – 12cos⁡2φ=0\frac{1}{2}\cos^{2}\varphi = 0 is greatest is-

A

{π,3π2,2π,3π}\left\{ \pi,\frac{3\pi}{2},2\pi,3\pi \right\}

B

{π , 3π}

C

{2π, 5π/4}

D

{3π2}\left\{ \frac{3\pi}{2} \right\}

Answer

{3π2}\left\{ \frac{3\pi}{2} \right\}

Explanation

Solution

α2 + β2 = (sin φ - 1)2 + 2 cos2 φ

= 3 – 2 sin φ – sin2φ = 4 – (sin φ + 1)2

Which is greatest when sin φ = –1

So, φ = 3π / 2