Let and . If is a quadratic equation whose roots are and , then the value of…

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Let

\alpha=\max_{x\in\mathbb{R}}\{8^{2\sin3x}\cdot4^{4\cos3x}\}

and

\beta=\min_{x\in\mathbb{R}}\{8^{2\sin3x}\cdot4^{4\cos3x}\}

. If

8x^2+bx+c=0

is a quadratic equation whose roots are

\alpha^{1/5}

and

\beta^{1/5}

, then the value of

c-b

is (a)

42

(b)

47

(c)

43

(d)

50