Show that x2 + 3 and x2 + x + 1 over Q have same splitting field.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 21E
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Question
Don't give below answer, again give worng answer ready for multiple downvote. Need correct answer, Show that x2 + 3 and x2 + x + 1 over Q have same splitting field.
![Solution
Let
P(X) =
x²+3 =
has splitting field
Q(Bi)
80
again
les
(-1-531)
2
Psatfh as eplitting field
Q (N3,i]
Here
Hence Babynomial Pica) and P2(X) foth hare
Rome splitting field Q[53, i] Ang](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe8d7d617-b8c1-467f-af7d-35ae6af3e84b%2F82b314cb-fc2d-4b25-8526-2f9db1eb4671%2Fhln11z_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Solution
Let
P(X) =
x²+3 =
has splitting field
Q(Bi)
80
again
les
(-1-531)
2
Psatfh as eplitting field
Q (N3,i]
Here
Hence Babynomial Pica) and P2(X) foth hare
Rome splitting field Q[53, i] Ang
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