The Roots Are Right There!

Algebra Level 4

\[x^3 + ax^2 + bx + c = 0\]

Nonzero integers \(a\), \(b\), and \(c\) are the roots of the above equation. If \(\alpha\) and \(\beta\) are the roots of the equation \(ax^2 + bx + c = 0\), what is \(\alpha^2 + \beta^2\)?

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