Transforming a Quartic Equation to the Binomial Form

The classical method of using Tschirnhaus transformation for transforming a quartic equation to the binomial form results in a sextic equation in one of the parameters of the transformation. Extracting the resolvent cubic equation from the sextic equation becomes an uphill task. A new method of transformation is proposed in this paper for transforming a quartic equation to the binomial form, wherein the resolvent cubic equation is derived explicitly and subsequently the quartic equation is transformed to the binomial form.