Testwiki:Reference desk/Archives/Mathematics/2016 July 25

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July 25

Roots of Polynomial-like Function

How should I find the roots of a function of the form $f:ℝ\to ℝ$, $f(x)=\sum _{i=1}^n{a}_i\cdot x^{\frac{1}{i}}$? (where $\{a_i\}$ are constant coefficients)31.154.81.45 (talk) 10:33, 25 July 2016 (UTC)

It is a polynomial already only very slightly disguised. Take the least common multiple of all the i values where $a_i$ is non-zero, call that L and substitute $y=x^{\frac{1}{L}}$ into what you have to give a polynomial in y. Dmcq (talk) 10:44, 25 July 2016 (UTC)

It's a great idea! Thank you! 31.154.81.45 (talk) 11:38, 25 July 2016 (UTC)