Get all roots of a 6th degree polynom numerical

Question

I have a polynomial of the 6th degree. For this Polynom, I want to get all real roots. My problem is that all the Methods I read about are only to get one root. Is there a way how I could get all the roots?

For example: With a polynom of 5th degree I can get the derivation. Solve it explicit and then use the solutions to get the intervals for the Newton Method.

Is there maybe also a way to solve this problem with a polynomial of 6th degree?

Thanks for your Help

Answer 1

The Durand-Kerner and Aberth-Ehrlich methods find all roots simultaneously and are as easy to implement as Newton’s method. Both methods are mentioned on this overview page.