Alphabet Roots

Calculus Level 3

If α\alpha and β\beta are roots of the equation x2px+q=0x^{2}-px+q=0 then

(α+β)x12(α2+β2)x2+13(α3+β3)x3(\alpha+\beta)x-\frac{1}{2}(\alpha^{2}+\beta^{2})x^{2}+\frac{1}{3}(\alpha^{3}+\beta^{3})x^{3}- \ldots is equal to?

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