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.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.5: Applications Of Inner Product Spaces
Problem 91E
icon
Related questions
Question
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.)
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,