Question 5. (a) Given the mapping 0 : C→C defined by 0(a + bi) = a -bi for all a, b € R. Show that is an automorphism of C. (b) Express the polynomial 3x4 - 4x³+4x -3 as a product of factors over R. Then express this polynomial as a product of factors over C. (c) Prove or disprove: The integral domain Z[√5], +, > is well-ordered.

Question 5. (a) Given the mapping 0 : C→C defined by 0(a + bi) = a -bi for all a, b € R. Show that is an automorphism of C. (b) Express the polynomial 3x4 - 4x³+4x -3 as a product of factors over R. Then express this polynomial as a product of factors over C. (c) Prove or disprove: The integral domain Z[√5], +, > is well-ordered.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.4: Zeros Of A Polynomial

Problem 1E: 1. Find a monic polynomial of least degree over that has the given numbers as zeros, and a monic...

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