Lesson Plan: Real and Complex Roots of Polynomials Mathematics
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to find the number and type of roots of polynomials and how to find unknown coefficients if the roots are given.
Students will be able to
- understand the definition of the root of a polynomial,
- understand that the degree of a polynomial tells us the number of roots, including repeated roots,
- find the number of roots of a polynomial by using Descartes’ rule of sign change,
- find the roots of polynomials using
- synthetic division,
- understand that if a complex number is a root of a polynomial, then its conjugate is also a root,
- find the lowest degree polynomial with integer coefficients given the roots,
- find unknown coefficients of a polynomial given its roots.
Students should already be familiar with
- factoring quadratics and solving quadratic equations,
- solving quadratic equations with complex solutions.
Students will not cover
- graphing polynomial functions.