Geodesic
Comparative analysis of solutions to $3^{rd}$ and $4^{th}$ order algebraic equations
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 16 (2016) no. 1, pp. 14-28 Cet article a éte moissonné depuis la source Math-Net.Ru

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Three methods of solving a cubic equation are analyzed: del Ferro–Tartaglia’s, Vieta’s, and F. Klein’s. Much attention is given to the irreducible case. Three methods of solving a quartic equation are compared: Ferrari–Cardano’s, Descartes’, and Euler’s. A new derivation of Euler’s formulas for the roots of a quartic algebraic equation is given. Some new methods of symbolic computation of roots of cubic and quartic equations are proposed.
Keywords: cubic, resolvent.
Mots-clés : quartic equation, Cardano’s formula, discriminant 
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N. S. Astapov; I. S. Astapov. Comparative analysis of solutions to $3^{rd}$ and $4^{th}$ order algebraic equations. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 16 (2016) no. 1, pp. 14-28. http://geodesic.mathdoc.fr/item/VNGU_2016_16_1_a1/

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