2) Let f(T) e Q[T] be an irreducible polynomial of degree n > 1. Show that f(T) has n different roots in C.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 2E
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2) Let f(T) e Q[T] be an irreducible polynomial of degree n > 1. Show
that f(T) has n different roots in C.
(Hint: consider the gcd of f(T) and its derivative.)
Transcribed Image Text:2) Let f(T) e Q[T] be an irreducible polynomial of degree n > 1. Show that f(T) has n different roots in C. (Hint: consider the gcd of f(T) and its derivative.)
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