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 
.
