How are the roots of a complex polynomial of degree > 4 actually found

Asked Apr 26 '22 at 16:06

Active Apr 26 '22 at 16:08

Viewed 40 times

I know that there are no general formulas for finding the roots of a complex polynomial of degree greater than 4. This site contains many questions about the roots of specific polynomials in this category.

The fundamental theorem of algebra says that such roots exist. How do people go about finding them? Is there something like Newton's method for complex polynomials?

edited Apr 26 '22 at 16:08

KReiser

65,137

asked Apr 26 '22 at 16:06

lewis robinson

In fact, Newton's method works also in the complex numbers, but not always. I am not aware of other methods in the complex numbers. – Peter Apr 26 '22 at 16:10
Wikipedia: Root-finding algorithms – Robert Israel Apr 26 '22 at 16:11
Answer depends on what is the goal. If you need to find exact root value in closed form, it is not always possible. But for specific polynomials it is possible, for example $az^5+b$ roots are easy to find. If you need to find proximate values of roots, then you can use numerical methods. – Ivan Kaznacheyeu Apr 26 '22 at 16:34
Ivan: Thanks. How about a link to the numerical methods you favor? – lewis robinson Apr 26 '22 at 18:26

How are the roots of a complex polynomial of degree > 4 actually found

0 Answers0