Polynomial Equations (Equations of Higher Degree)

by M. Bourne

This chapter discusses methods for solving higher degree polynomial equations.

In the study of polynomial equations, the most important thing is to understand what "solution of an equation" means. For equations of higher degree, allow for many solutions. The maximum number of solutions you can get is the degree of the polynomial.

After you finish this chapter, you should be able to use a Computer Algebra System to find solutions, either...

polynomial graph

(a) Graphically, or
(b) Using the CAS directly.

Applications of Root Finding:

  • modelling
  • curve fitting
  • instrumentation
  • ecological and industrial safety
  • industrial maintenance and control problems

Historical Solutions...

This section contains some dinosaur mathematics (that is, it is extinct). With software tools, there is no need to churn through pages of algebra solving these things. It is more important to know what it all means and how you can apply it to real problems.