Roots - real or complex ?

Algebra Level 3

If α\alpha is one of the non-real seventh roots of unity, then find the discriminant of the monic quadratic equation with the roots α+α2+α4\alpha+\alpha^2+\alpha^4 and α3+α5+α6.\alpha^3+\alpha^5+\alpha^6.

Details and Assumptions:

  • The discriminant of a quadratic equation ax2+bx+c=0ax^2+bx+c=0 is b24ac.b^2-4ac.
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