Alphabet Roots

Calculus Level 3

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

$(\alpha+\beta)x-\frac{1}{2}(\alpha^{2}+\beta^{2})x^{2}+\frac{1}{3}(\alpha^{3}+\beta^{3})x^{3}- \ldots$ is equal to?

\ln(px^{2}-qx+1)

\ln(qx^{2}+px+1)

\ln(px^{2}+qx+1)

\ln(qx^{2}-px+1)

\ln(px^{2}+qx-1)

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