MathDB
Putnam 2005 A3

Source:

December 5, 2005
PutnamalgebrapolynomialStanfordcollegefunctiongeometry

Problem Statement

Let p(z)p(z) be a polynomial of degree n,n, all of whose zeros have absolute value 11 in the complex plane. Put g(z)=p(z)zn/2.g(z)=\frac{p(z)}{z^{n/2}}. Show that all zeros of g′(z)=0g'(z)=0 have absolute value 1.1.
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