The Roots Are Right There!

Algebra Level 4

x3+ax2+bx+c=0x^3 + ax^2 + bx + c = 0

Nonzero integers aa, bb, and cc are the roots of the above equation. If α\alpha and β\beta are the roots of the equation ax2+bx+c=0ax^2 + bx + c = 0, what is α2+β2\alpha^2 + \beta^2?

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