A simulation technique called multi stage Monte Carlo optimization (MSMCO) is used to approximate the roots to a 300 degree polynomial. MSMCO consists of repeated random searches in an ever-narrowing focused region centred about the “best answer so far”. This process continues until a good approximate root is produced. Then it is factored out of the polynomial equation and the search for the next root begins in a similar fashion. Multi stage is a general purpose solution technique that can work on a wide variety of problems. Its best potential for application is for the approximate solutions to difficult problems.