If `alpha` and `beta` are the roots of the equation `x^2-px + q = 0` then the value of `(alpha+beta)x -((alpha^2+beta^2)/2)x^2+((alpha^3+beta^3)/3)x^3+...` is

Options

A. `log(1+px+qx^(2))`
B. `log(1+qx+px^(2))`
C. `log(x^(2)+px+q)`
D. none of these

Explanation

To solve the problem, we need to find the value of the series given by:

\[ (\alpha + \beta)x - \frac{(\alpha^2 + \beta^2)}{2}x^2 + \frac{(\alpha^3 + \beta^3)}{3}x^3 + \ldots \]

where \(\alpha\) and \(\beta\) are the roots of the equation \(x^2 - px + q = 0\).

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