A10 2. Consider the following set of linear polynomials with rational coefficients:E₁ {ar+ba.be Q. a 0}=(a).Prove that E₁ is countably infinite.(b).In general, let E, denote the set of polynomials of degree n.with rational coefficients. Prove that. En is countably infinite for all n ≥ 0.

The set E1 is defined as follows. E1=ax+b | a, b∈ℚ, a≠0 The set is linearly polynomial with rational…

Answered: 2. Consider the following set of linear…

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 34E

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2. Consider the following set of linear polynomials with rational coefficients: E = {ar+bla.be Q. a 0} (a). Prove that E₁ is countably infinite. (b). In general, let E, denote the set of polynomials of degree n with rational coefficients. Prove that. En is countably infinite for all n ≥ 0.