Let K be the splitting field of f(x) = F(x)and let p(x) be an irreducible factor off(x) in F(x). If the roots of p(x) area₁, A2,... 0₁, then for each i there existsan automorphism o¡ in G(K, F) such that0₁(α₁) = 0₁.i

Since p(x) is an irreducible factor of f(x)∈F[x], then every root of p(x) is a root of f(x), so it…

Answered: Let 'R be the splitting field of f(x) €…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let 'R be the splitting field of f(x) € F and let p(x) be an irreducible factor of f(x) in F(x). If the roots of p(x) are α₁, α2,... O¡, then for each i there exists an automorphism o; in G(K, F) such th