Some methods of solving cubic equations

• Main Authors: Cornejo, Ma. Eliza, Gabelo, Hazel
• Format: text
• Language: English
• Published: Animo Repository 1995
• Subjects: Problem solving; Equations, Cubic; Functions, Algebraic
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16246
• Institution: De La Salle University

This thesis presents those methods in solving cubic equations. It is simple to follow and easy to understand.The first method, developed by Girolamo Cardano, called the Cardan's formula, uses derivations and substitutions to arrive at the roots. The Taylor's formula is also used and assuming unknown variables helped in the derivations and substitutions.The second method, developed by Joseph Mandelbaum makes use of a formula similar to the quadratic formula to solve cubic equations with one or more rational roots. This method shortens the process of finding the roots considerably.The third method by R.S. Luthar tackles the solution of Hari Ram Luddhar to the cubic equation. It uses the fact that a cubic polynomial with a rational zero can always be represented as the product of a linear factor and a quadratic factor.The results of this study indicate that the method used by J. Mandelbaum and R.S. Luthar for getting the roots are simpler to apply. However, they work only for a class of cubic equations. Further studies must be conducted to extend these methods to equations of higher degree.