If f (x) is any polynomial of degree n21 over a field F, then there exists an extension K of F such that f (x) has n roots in K and [K: F]
If f (x) is any polynomial of degree n21 over a field F, then there exists an extension K of F such that f (x) has n roots in K and [K: F]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![If f (x) is any polynomial of degree n 21 over a field
F, then there exists an extension K of F such that f (x) has n roots in K and
[K:F]<n!.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8326930b-699f-4bf2-b8b5-e4d18bba78ec%2F3f78cf5b-99b3-4c2b-9587-dd7727fce466%2Fvfl3zr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:If f (x) is any polynomial of degree n 21 over a field
F, then there exists an extension K of F such that f (x) has n roots in K and
[K:F]<n!.
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