Students generate random polynomials and observe the distribution of the zeros on the complex plane. From the distributions students are able to draw conclusions about the zeros, and therefore roots, of a polynomial in order to gain a better visual understanding of the Fundamental Theorem of Algebra.
Consider conjugate roots for polynomials with real coefficients and the logical extension to understand the Fundamental Theorem of Algebra.
Polynomial, factor, repeated factor, multiplicity, conjugate, root, zeros
About the Lesson
Students start by factorising some basic quadratic functions followed by products of these quadratic in order to build an understanding of the formulation of factors in larger polynomials. As the factors, with multiplicity, are explored the notion of the quantity of factors is considered. The polynomials are then factored over C, followed by random polynomials and subsequent zeros on the Argand plane with a view to developing a conjecture pertaining to the Fundamental Theorem of Algebra.