please solve both neatly Let E be a field whose elements are the distinct zeros of x2" – x in Z2.1. If K is an extension of E of degree 2, what is |K]?2. If E is an extension of F of degree 2, what is |F|?

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Answered: Let E be a field whose elements are the…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.6: Algebraic Extensions Of A Field

Problem 1TFE: True or False Label each of the following statements as either true or false. Every polynomial...

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Let E be a field whose elements are the distinct zeros of x2° – x in Z2. 1. If K is an extension of E of degree 2, what is |K|? 2. If E is an extension of F of degree 2, what is |F|?