$ P\in C[X],\ P=X^3-X^2+6X-1$ and $ \alpha_1,\alpha_2,\alpha_3$ it’s roots. Find $ \alpha_1^5+\alpha_2^5+\alpha_3^5$ . I know there are some recursive formulas to solve this but I cannot remember them or their author.

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# Polynomial roots equation

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$ P\in C[X],\ P=X^3-X^2+6X-1$ and $ \alpha_1,\alpha_2,\alpha_3$ it’s roots. Find $ \alpha_1^5+\alpha_2^5+\alpha_3^5$ . I know there are some recursive formulas to solve this but I cannot remember them or their author.

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