Let P(z) = z" +am-12"-1 + ... + a1z + ao be a polynomial of degree n 2 1 with a; # 0 for at %3D least one i. Prove that there exists a point z* such that 2*| = 1 and |P(z*)| > 1.
Let P(z) = z" +am-12"-1 + ... + a1z + ao be a polynomial of degree n 2 1 with a; # 0 for at %3D least one i. Prove that there exists a point z* such that 2*| = 1 and |P(z*)| > 1.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.1: Polynomials Over A Ring
Problem 12E: a. Find a nonconstant polynomial in Z4[ x ], if one exists, that is a unit. b. Find a nonconstant...
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