# Roots - real or complex ?

Algebra Level 4

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


Details and Assumptions:

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