Quintics with Symmetries

It has been known for a long time that there is no general analytical solution to determine zeros of quintics (polynomials of degree 5) by radical expressions. However, one may assume that certain classes of quintic equations can actually be solved if corresponding specific resolvents for those can be found.

If more than two zeroes of a quintic equation are located in a circular symmetric fashion, be it centrally around 0 or an arbitrary value in the field of complex numbers, it indeed turns out that resolvents can be determined; for all of these, it is possible to determine the exact zeroes by those specific resolvents and subsequent equations of lower degree than 5 which are presented in this book. In addition, various examples are provided to show how quintic equations that fulfil the respective conditions can be solved.