A simple approach to solving cubic equations

Abstract

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.