ROOTS OF POLYNOMIALS

 

 

Finding the roots of polynomials, or "solving algebraic equations", is among the oldest problems in mathematics.

 

The goal in this project is to describe some of the history, mathematically what is involved and (except for part 4) an outline of the solution for each of the following. (We assume that the coefficients are real numbers throughout.)

 

  1. Finding roots of linear and quadratic polynomials, including the concepts of zero, negative and complex numbers.

 

  1. Finding roots of cubic polynomials and Tartaglia.

 

  1. Finding roots of quartic polynomials using part b.

 

  1. The general impossibility of finding roots of quintic polynomials and Galois.

 

For a, See 'Numbers' by Ebbinghaus et al., and for the others, see 'Rings, Fields and Groups' by R. Allenby.

 

 

 

Developed by Graham Norton.

 

 

http://www.maths.uq.edu.au