| Obtaining solutions to polynomial equations is essential to the study of mathematics. In the realm of complex numbers, every polynomial equation has a solution. Of particular interest are the zeros of polynomials, which are what we will look at in this thesis.; Using the (Extended) Fundamental Theorem of Algebra we will prove that a polynomial of degree n has exactly n number of zeros, counting multiplicities. With this fact in mind, we will then utilize Rouche's Theorem to develop a formula for finding an outer bound for the zeros of certain complex polynomials. |
