A Tschirnhausen Transformation can be used to algebraically transform a general Quintic Equation to the form

(1) 
In practice, the general quintic is first reduced to the Principal Quintic Form

(2) 
before the transformation is done. Then, we require that the sum of the third Powers of the
Roots vanishes, so . We assume that the Roots of the BringJerrard
quintic are related to the Roots of the Principal Quintic Form by

(3) 
In a similar manner to the Principal Quintic Form transformation, we can express the
Coefficients in terms of the .
See also Bring Quintic Form, Principal Quintic Form, Quintic Equation
© 19969 Eric W. Weisstein
19990526