7 Quadratic polynomial factors should be typed as (x^2+ax+b)(x^2+cx+d)( :) Factor f(x) = x¹-2x³-x² - 2x - 2 € Q[x] into two irreducible quadratic polynomials over Q. Hint: Factor as (x² + ax + b)(x² + cx + d) where a < c. Enter your answer 8 Find a splitting field for the polynomial in the previous item. Write in the form Q(u, v) and follow the format for writing radicals. Enter your answer (
7 Quadratic polynomial factors should be typed as (x^2+ax+b)(x^2+cx+d)( :) Factor f(x) = x¹-2x³-x² - 2x - 2 € Q[x] into two irreducible quadratic polynomials over Q. Hint: Factor as (x² + ax + b)(x² + cx + d) where a < c. Enter your answer 8 Find a splitting field for the polynomial in the previous item. Write in the form Q(u, v) and follow the format for writing radicals. Enter your answer (
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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PLEASE ANSWER 7 NEED THIS ASAP
![7
Quadratic polynomial factors should be
typed as (x^2+ax+b)(x^2+cx+d)( :)
Factor f(x) = x¹-2x³x² - 2x - 2 € Q[x] into two irreducible quadratic polynomials over Q.
Hint: Factor as (x² + ax + b)(x² + cx + d) where a < c.
Enter your answer
8
Find a splitting field for the polynomial in the
previous item. Write in the form Q(u, v) and
follow the format for writing radicals.
Enter your answer
9
The Galois group of the polynomial f over
the rationals Q in the previous example is
isomorphic to a subgroup H of order 4 in
S_4. Describe this subgroup by listing down
the permutations enclosed in a pair of
braces. No spaces in writing
permutations. {w,x,y,z} where each of x,y,z
are non-identity permutations.
(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85584a28-cec6-4119-b265-5692abdcabb3%2Fb95128f5-c588-454d-9deb-f22f48f15eab%2Ffrow1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7
Quadratic polynomial factors should be
typed as (x^2+ax+b)(x^2+cx+d)( :)
Factor f(x) = x¹-2x³x² - 2x - 2 € Q[x] into two irreducible quadratic polynomials over Q.
Hint: Factor as (x² + ax + b)(x² + cx + d) where a < c.
Enter your answer
8
Find a splitting field for the polynomial in the
previous item. Write in the form Q(u, v) and
follow the format for writing radicals.
Enter your answer
9
The Galois group of the polynomial f over
the rationals Q in the previous example is
isomorphic to a subgroup H of order 4 in
S_4. Describe this subgroup by listing down
the permutations enclosed in a pair of
braces. No spaces in writing
permutations. {w,x,y,z} where each of x,y,z
are non-identity permutations.
(
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