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Let F be a field and f(x) E F[x] be of degree

Let F be a field and f(x) E F[x] be of degree

Advanced Engineering Mathematics
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 F be a field and f(x) E F[x] be of degree n> 1. Then the exists a field extension K of F and a1,..., an E K such that (a) f(x) = c(x-a1)... (x-an) for some c E F. (b) K= F(a1,..., an) and dimp(K) ≤n!..
Transcribed Image Text:Let F be a field and f(x) E F[x] be of degree n> 1. Then the exists a field extension K of F and a1,..., an E K such that (a) f(x) = c(x-a1)... (x-an) for some c E F. (b) K= F(a1,..., an) and dimp(K) ≤n!..
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