<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The classic method of solving the cubic and the quartic equations using Tschirnhaus transformation yields true as well as false solutions. Recently some papers on this topic are published, in which methods are given to get only the true solutions of cubic and quartic equations. However these methods have some limitations. In this paper the author presents a method of solving cubic and quartic equations using Tschirnhaus transformation, which yields only the true solutions. The proposed method is much simpler than the methods published earlier.</p>
</abstract>

The classic method of solving the cubic and the quartic equations using Tschirnhaus transformation yields true as well as false solutions. Recently some papers on this topic are published, in which methods are given to get only the true solutions of cubic and quartic equations. However these methods have some limitations. In this paper the author presents a method of solving cubic and quartic equations using Tschirnhaus transformation, which yields only the true solutions. The proposed method is much simpler than the methods published earlier.

A simpler method to get only the true solutions of cubic and quartic equations using Tschirnhaus transformation

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

The classic method of solving the cubic and the quartic equations using Tschirnhaus transformation yields true as well as false solutions. Recently some papers...

A simpler method to get only the true solutions of cubic and quartic equations using Tschirnhaus transformation

Published Online: Sep 25, 2022

Page range: 51 - 56

Received: Mar 30, 2022

Accepted: Aug 08, 2022

DOI: https://doi.org/10.2478/aupcsm-2022-0005

Keywords
Tschirnhaus transformation, true solutions, cubic equations, quartic equations, false solutions

© 2022 Raghavendra G. Kulkarni, published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

A simpler method to get only the true solutions of cubic and quartic equations using Tschirnhaus transformation

Published Online: Sep 25, 2022

Page range: 51 - 56

Received: Mar 30, 2022

Accepted: Aug 08, 2022

DOI: https://doi.org/10.2478/aupcsm-2022-0005

KeywordsTschirnhaus transformation, true solutions, cubic equations, quartic equations, false solutions

© 2022 Raghavendra G. Kulkarni, published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Keywords
Tschirnhaus transformation, true solutions, cubic equations, quartic equations, false solutions