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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