MATLAB® 3.5 had two different methods for finding the roots of polynomials. The original root finder in MATLAB,
roots, was a short M-file that simply set up the companion matrix and used the built-in
eig function to find its eigenvalues. A second polynomial root finder,
roots1, based on Laguerre’s method, was introduced later.
In this article, originally published in 1991, Cleve Moler explains serious flaws with this second method that led to unacceptable results. The
roots1 function was removed in MATLAB 4.0.