Let and . If ,…

MATHEMATICS · Single correct · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

Let

f(x) = x^{13} + 2x^{12} + 3x^{11} + \dots + 13x + 14

and

\alpha = \cos \frac{2\pi}{15} + i \sin \frac{2\pi}{15}

. If

N = f(\alpha)f(\alpha^2)\dots f(\alpha^{14})

, then (1) number of divisors of

N

is 144 (2) number of divisors of

N

is 196 (3) number of divisors of

N

which are perfect squares of 49 (4) number of divisors of

N

which are perfect square of 12