Finding roots of characteristic polynomial of 3x3 matrix

Question

I have never learned how to solve cubic equations and unfortunately need to do it in an upcoming exam for finding eigenvalues.

I have been searching on the web for good resources, but whenever I find a trick on how to find the roots of a cubic polynomial I find a polynomial for which none of the methods is applicable.

I don't have any literature on this topic, can anybody please guide me to a good text or web source where I can pick this up relatively quickly please?

Answer 1

There does exist a general formula for the roots of a cubic polynomial, you can find it on the wikipedia article. However, usually, it is much easier to guess one root and then reduce the polynomial to a quadratic.

In all my exams, I never once had to use the general formula for cubic roots, as every time, the matrix is set up in such a way that one root is easy to find.