Recently I came across a situation where I needed to solve a 4th degree polynomial equation in .NET, and to my surprise I couldn't find any code written in C# or VB .NET that contained the algebraic formulas (I did find some C++ and C# implementations , but they were numerical solutions and I didn’t want to use them).
The algebraic formulas are nasty, and would definitely clog up your day if you ever had a need for one, so I decided to share it with you. I also have a rather lengthy story to follow it, as I have read "The equation that couldn’t be solved" by Mario Livio. The title of the book refers to the story of the insolvability of the 5th degree polynomial equation, but it also goes through the historical development of the solutions to lower degree polynomial equations.
I won’t give any explanations of how these formulas were derived, as the formulas get quite lengthy, so long that in fact that even Tartaglia (one of the people that had a part in solving the cubic equation) had problems in remembering all the rules he had discovered.
Polynomial Equation Solver - CodeProject