# Roots

Algebra Level 4

If $$\alpha$$ and $$\beta$$ are the real roots of $$x^2 + px + q = 0$$ and $$\alpha^4$$ and $$\beta^4$$ are the roots of $$x^2 - rx + s = 0,$$ then the equation $$x^2 - 4qx + 2q^2 - r = 0$$ always has what kind of roots?

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