Study on a Particular Form of Cubic Equation

Authors- Arnab Gain

Abstract- In this paper the general form of cubic equation has been modified into a particular form and has been thoroughly studied. To evaluate exact roots of the modified form, a simplified formula has been derived and presented. This derived formula is similar to that of Sridharacharya’s formula for solving quadratic equation and the similarities has been pointed out in this paper. Furthermore this particular form behaves in a special manner when Cardan’s method is applied on it for finding the roots. In the preliminaries section basic definitions, rules for round off and the Cardan’s method for solving cubic equations have been stated in this paper for better understanding purposes. Apart from finding out the roots of the special types of cubic equation, the nature of the roots has also been discussed here. To illustrate utility of the derived formula appropriate examples have been provided. A brief historical background of evaluation of cubic equation is also given in the introduction section and names of various well known methods to solve the cubic equations are also mentioned here. This derived formula will be very helpful for solving the particular types of cubic equations discussed here. More over the derived formula is very easy to remember and recall in the time of need. Some interesting observations have been made throughout the paper. The similarity of the derived formula with that of Sridharacharya’s formula is matter of interest in the paper.

DOI: /10.61463/ijset.vol.12.issue3.177