If `alpha, beta, gamma` are the roots of the equatiion `x^(3)-px^(2)+qx-r=0` find
(i) `sumalppha^(2)` (ii) `sumalpha^(2) beta` (iii) `sum alpha^(3)`

Explanation

To solve the problem, we will use Vieta's formulas, which relate the coefficients of a polynomial to sums and products of its roots. Given the polynomial equation \(x^3 - px^2 + qx - r = 0\), we know the following:

1. The sum of the roots \( \alpha + \beta + \gamma = p \)
2. The sum of the products of the roots taken two at a time \( \alpha\beta + \beta\gamma + \gamma\alpha = q \)
3. The product of the roots \( \alpha\beta\gamma = r \)

Now, we will find the required expressions step by step.

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