If , where , find the quadratic equation whose roots are and…

MATHEMATICS · Subjective · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

If

a = \cos \left( \frac{2\pi}{7} \right) + i \sin \left( \frac{2\pi}{7} \right)

, where

i = \sqrt{-1}

, find the quadratic equation whose roots are

\alpha = a + a^2 + a^4

and

\beta = a^3 + a^5 + a^6

.

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