Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-20T01:38:30.421Z Has data issue: false hasContentIssue false

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: [email protected]
Gerry Leversha
Affiliation:

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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
3.Yardley, P. D., Graphical solution of the cubic equation developed from the work of Omar Khayyam, Bull. Inst. Math. Appl. 26, (1990) pp. 122125.Google Scholar
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