Solvable Brioschi resolvents
The Brioschi resolvent y(5) - 10Zy(3) + 45Z(2)y - Z(2) is a key component of an algorithm for calculating the roots of a general quintic polynomial. It is obtained from the general quintic polynomial by applying two Tschirnhausen transformations. In this paper it is shown that if the quintic polynomial is a solvable polynomial, then its associated parameter Z in the Brioschi resolvent satisfies Z = g(t) where g(t) is a rational function in Q(t) and t is chosen from an appropriate field.
solvable quintic brioschi quintic resolvent sextic parametrization