1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Oct 4, 2012 #1
    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. jcsd
  3. Oct 4, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    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).
  4. Oct 4, 2012 #3
    That makes total sense now! Thanks, I have the problem solved now!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook