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July 25

Roots of Polynomial-like Function

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

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)[reply]

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