Let \(\omega\) be a complex number such that \(\omega^7 = 1\) and \(\omega \neq 1\). Let \(\alpha = \omega + \omega^2 + \omega^4\) and \(\beta = \omega^3 + \omega^5 + \omega^6\). Then \(\alpha\) and \(\beta\)

are roots of the quadratic x^2 + px + q = 0 for some integers p and q. Find p and q.

Here's an interesting problem I've been stumped on, any pointers and help? Thanks!

rubikx2910 Feb 24, 2020