Solvability of cubic and quartic equations using one radical
History and Overview
2015-11-16 v3
Abstract
Theorem. An irreducible cubic polynomial with rational coefficients has a root in a one step radical extension of Q if and only if the discriminate is a square of a rational number. Theorem. An irreducible polynomial x^4+px^2+qx+s with rational coefficients q\ne0, p and s has a root in a one step radical extension of Q if and only if the cubic resolution has rational root t such that t>p/2 and A:=16(t^2-s)^2-(t^2-s)(2t+p)^2 is a square of a rational number.
Cite
@article{arxiv.1411.4990,
title = {Solvability of cubic and quartic equations using one radical},
author = {Danil Akhtyamov and Ilya Bogdanov},
journal= {arXiv preprint arXiv:1411.4990},
year = {2015}
}
Comments
3 pages