a. Give the smallest extension of Q that contains all the zeros of x4 - 2x2 – 15.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 38E
Related questions
Question
![Do as asked.
a. Give the smallest extension of Q that contains all the zeros of x4 – 2x2 – 15.
b. Let m, n be positive integers. Show that the real numbers em and e are algebraic over
Q(e"). [Here, e is Euler's number.]
c. Let a =
V7+4/3. Show that [Q(a) : Q] = 2.
d. Let p be a prime. Give all the subfields of F,20 and sketch its subfield lattice.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18c51d48-2201-40b6-bcbd-9606bca209af%2F29a225cc-927f-41a8-a464-e212c1e6bf8f%2Fmmtawr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Do as asked.
a. Give the smallest extension of Q that contains all the zeros of x4 – 2x2 – 15.
b. Let m, n be positive integers. Show that the real numbers em and e are algebraic over
Q(e"). [Here, e is Euler's number.]
c. Let a =
V7+4/3. Show that [Q(a) : Q] = 2.
d. Let p be a prime. Give all the subfields of F,20 and sketch its subfield lattice.
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