Équation sextique

Équation du sixième degré

Une équation sextique est une équation polynomiale de degré 6^[1] de la forme $ax^{6}+bx^{5}+cx^{4}+dx^{3}+ex^{2}+fx+g=0$ , où $a,b,c,d,e,f$ sont des coefficients réels ou complexes (ou appartenant à n'importe quel corps). On a spécifiquement $a\neq 0$ .

Une telle équation est obtenu à partir d'un polynôme $P=f(x)$ , où $f(x)$ est une fonction sextique de la forme $ax^{6}+bx^{5}+cx^{4}+dx^{3}+ex^{2}+fx+g$ , $a\neq 0$ .

Selon le théorème d'Abel, la plupart des équations sextiques ne sont pas résolubles par radicaux^[2]. D'autres, comme les équations suivantes, le sont :

ax^{6}+b=0,\quad a\neq 0

, qui peut se ramener au cas linéaire

ax^{6}+bx^{3}+c=0,\quad a\neq 0

, qui peut se ramener au cas quadratique

Liens externes

(en) Eric W. Weisstein, « Sextic Equation », sur MathWorld

Notes et références

↑ Raghavendra G. Kulkarni, « Solving sextic equations », Atlantic Electronic Journal of Mathematics, vol. 3, n^o 1,‎ 2008, p. 193–209 (lire en ligne [PDF], consulté le 14 janvier 2023)
↑ « Beweis der Unmöglichkeit, algebraische Gleichungen von höheren Graden als dem vierten allgemein aufzulösen. », Journal für die reine und angewandte Mathematik (Crelles Journal), vol. 1826, n^o 1,‎ 1^er janvier 1826, p. 65–84 (ISSN 0075-4102 et 1435-5345, DOI 10.1515/crll.1826.1.65, lire en ligne, consulté le 14 janvier 2023)

v · m

Polynômes

Degrés

Fonctions	Nulle Constante Linéaire Affine Du second degré Cubique Inverse
Équations	Linéaire Du second degré Cubique Quartique Quintique Sextique

Nombre de termes

Algorithmes

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