Quintics with Symmetries

Beschreibung

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, certain classes of quintic equations can be solved, including both reducible and irreducible cases. In this book, a wide range of reducible quintics is analysed which can be linked to symmetric settings of zeroes. Specifically, if there are two square roots, or if more than two zeroes of a quintic equation are located in a circular symmetric fashion - be it centrally around 0 or an arbitrary point in the field of complex numbers - this corresponds, with the exception of a 5th roots scenario, to a reducible quintic. Solutions are provided by derived equations of lower degree than 5 which are presented in this book. In addition, various examples for quintic equations that fulfil the respective conditions are shown in detail.

Autor*in

Achim Plum
Achim Plum holds a degree (Diplom) from RWTH Aachen, Germany, in Computer Science with Mathematics as second discipline. For a long time, he had worked in different industries as a professional in Information Technology and Management; currently he works as a teacher. Beyond this, he stayed interested in mathematical topics and keeps studying further in Mathematics and related areas.

Themen in »Quintics with Symmetries«

Polynom Nullstellen Gleichung zeroes equation

Stimmen zu »Quintics with Symmetries«

Details

Link teilen