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A simple approach to solving cubic equations

Published online by Cambridge University Press:  14 June 2016

Fleur T. Tehrani
Affiliation:
Dept. of Electrical Engineering, California State University, Fullerton, 800 N. State College Boulevard, Fullerton, California 92831, USA e-mail: ftehrani@fullerton.edu
Gerry Leversha
Affiliation:
e-mail: g.leversha@btinternet.com

Extract

Finding the roots of cubic equations has been the focus of research by many mathematicians. Omar Khayyam, the 11th century Iranian mathematician, astronomer, philosopher and poet, discovered a geometrical method for solving cubic equations by intersecting conic sections [1]. In more recent times, various methods have been presented to find the roots of cubic equations. Some methods require complex number calculations, a number of techniques use graphical methods to find the roots [e.g. 2, 3] and some other techniques use trigonometric functions [e.g. 4]. The method presented in this paper does not use graphical techniques as in [2] and [3], does not involve complex number calculations, and does not require using trigonometric functions. By using this fairly simple method, the roots of cubic equations can be found in a short time without using complicated formulas.

Type
Research Article
Copyright
Copyright © Mathematical Association 2016 

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References

1.O'Connor, J. J. and Robertson, E. F., Khayyam, Omar, MacTutor History of Mathematics archive, accessed February 2016 at: http://www-history.mcs.st-andrews.ac.uk/history/Biographies/Khayyam.htmlGoogle Scholar
2.Henriquez, G., The graphical interpretation of the complex roots of cubic equations, Amer. Math. Monthly 42, (1935) pp. 383384.CrossRefGoogle Scholar
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4.Nickalls, R. W. D., A new approach to solving the cubic: Cardan's solution revealed, Math. Gaz. 77 (November 1993) pp. 354359.Google Scholar