Answered: Every nonconstant polynomial in F[x]…

Every nonconstant polynomial in F[x] has a root in every extension field of F, that is if K is an extension of F and f is a nonconstant polynomial in F[x], then f has a root in K.

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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Question

True or False

1. Every nonconstant polynomial in F[x] has a root in every extension field of F, that is if K is an extension of F and f is a nonconstant polynomial in F[x], then f has a root in K.
2. There is no proper intermediate field of ℝ and ℂ, i.e. there exists no field E such that ℝ ≤ E ≤ ℂ but ℝ ≠ E, E ≠ ℂ.
3. If [K:F]=p for some prime p and F ≤ E ≤ F, then F=E.

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