2014/11/15 by Danil Akhtyamov, Akhtyamov, Danil, Ilya I. Bogdanov +2
Computer Science · Mathematics · #12F05 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #History and Overview (math.HO) #Iterative Methods for Nonlinear Equations #Polynomial and algebraic computation #math.HO #msc:12F05
paper · pdf · doi:10.48550/arxiv.1411.4990
3 pages
openalex publication_date 2014/11/15 · arxiv created 2015/11/13 · arxiv updated 2015/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 x4+px2+qx+s with rational coefficients q≠0, 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(t2-s)2-(t2-s)(2t+p)2 is a square of a rational number.