1. Apr 16, 2009 #1

   oab729

   

   1. The problem statement, all variables and given/known data
   Show that for a polynomial of degree n, P(z), that for all z with |z| sufficiently large, there are positive constants c,d, s.t. c|z|^n < |P(z)| < d|z|^n
   
   
   2. Relevant equations
   
   
   
   3. The attempt at a solution
   Assume it is true for n-1.
   p(z)=az^n+q(z)
   Then for z with sufficiently large |z|, there exist e,f s.t. e|z|^(n-1) < |q(z)| < f|z|^(n-1).
   
   No idea how to continue.

    

   oab729, Apr 16, 2009
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3. Apr 17, 2009 #2

   Billy Bob

   

   Try doing |P(z)| < d|z|^n and c|z|^n < |P(z)| as two different problems. Use triangle inequality. Try it with actual example polynomials first if you're still lost.

    

   Billy Bob, Apr 17, 2009

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