Do we have some proper method to find sum of roots of the root of P(x)? Like say we have P(x) =$ x^3 -16x^2 + 57x+1$ say its root are a,b, c for finding $ a^{1/5} + b^ {1/5} +c^{1/5} $ do we have some method or i need to take power 5 and solve manipulating the terms ?
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Interesting. I would think there might be some results as an application of vieta's formula's – Mason Nov 17 '18 at 20:58
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https://www.desmos.com/calculator/x29fcpfahk – Mason Nov 17 '18 at 21:09
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No. I would think that there is not a general method of doing this: You will have to compute the roots and then compute the powers. For a polynomials with degree less than $4$ there is a formula for finding the roots: and thereby there is a formula for the sum of the roots raised to some power. For higher degree polynomials there is not a formula for this. – Mason Nov 17 '18 at 21:33
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so here can we find the value? – maveric Nov 18 '18 at 05:26
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Very similar to Sum of fifth roots of roots of cubic. – mathlove Nov 18 '18 at 06:08
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yes. almost duplicate. cant we solve completely by hands – maveric Nov 18 '18 at 09:21