Tschirnhausen Transformation

A transformation of a Polynomial equation which is of the form where and are Polynomials and does not vanish at a root of . The Cubic Equation is a special case of such a transformation. Tschirnhaus (1683) showed that a Polynomial of degree can be reduced to a form in which the and terms have 0 Coefficients. In 1786, E. S. Bring showed that a general Quintic Equation can be reduced to the form

In 1834, G. B. Jerrard showed that a Tschirnhaus transformation can be used to eliminate the , , and terms for a general Polynomial equation of degree .