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

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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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     author = {N. S. Astapov and I. S. Astapov},
     title = {Comparative analysis of solutions to $3^{rd}$ and $4^{th}$ order algebraic equations},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
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     publisher = {mathdoc},
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     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2016_16_1_a1/}
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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/