# Homework Help: Showing a polynomial has at least one zero outside the unit circle.

1. Oct 4, 2012

### jdinatale

The first thing that we should notice is that the leading coefficient $a_n = 1$. I was thinking about considering the factored form of p.

I googled, and there is an algorithm called the "Schur-Cohn Algorithm" that is suppose to answer exactly this, but I can't find any information on it or how to use it. Besides, this question is asked in an introduction to complex variables class, so we shouldn't have to use that algorithm.

Also, I found this questioned answered elsewhere, but I can't understand their solutions

2. Oct 4, 2012

### SammyS

Staff Emeritus
The second solution in that link looks reasonable.

What is p(0) ?

Suppose we write the zeros of p(z) as z1, z2, z3, ..., zn.

Write p(z) in factored form, and from that, set z=0 to find a different expression for p(0).

3. Oct 4, 2012

### jdinatale

That makes total sense now! Thanks, I have the problem solved now!