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

Authors

  • Raghavendra G. Kulkarni PES University

Keywords:

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

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.

References

Adamchik, Victor S., and David J. Jeffrey. "Polynomial transformations of Tschirnhaus, Bring and Jarrard." ACM SIGSAM Bulletin, 37, no. 3 (2003): 90-94.
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Dickson, Leonard Eugene. First course in the theory of equations. New York: John Wiley & Sons Inc., 1922.
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Kulkarni, Raghavendra G. "Picking genuine zeros of cubics in the Tschirnhaus method." Math. Gaz. 100, no. 547 (2016): 48-53.
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Kulkarni, Raghavendra G. "Tschirnhaus transformation method sans false solutions for solving cubics." Fasc. Math. No. 63 (2020): 39-43.
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Kulkarni, Raghavendra G. "A novel Tschirnhaus method to get only the true solutions of quartic equations." Lect. Mat. 39, no. 1 (2018): 5–9.
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Tschirnhaus, Ehrenfried W. "A method for removing all intermediate terms from a given equation", Acta Eruditorum, (1683): pp. 204-207. Translated by R. F. Green in ACM SIGSAM Bulletin 37, no. 1, (2003): 1-3.
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Published

2022-09-05

How to Cite

Kulkarni, R. G. (2022). A simpler method to get only the true solutions of cubic and quartic equations using Tschirnhaus transformation. Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica, 21, 51–56. Retrieved from https://studmath.uken.krakow.pl/article/view/9500

Issue

Vol. 21 (2022)

Section

Published

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