20. Find the splitting field for x^2-2sqrt(2)x+3 over Q(sqrt(2)). Find the roots first then simplify. Note: Q(sqrt(2),u) where u is a root. Then write the simplest form of this splitting field.
20. Find the splitting field for x^2-2sqrt(2)x+3 over Q(sqrt(2)). Find the roots first then simplify. Note: Q(sqrt(2),u) where u is a root. Then write the simplest form of this splitting field.
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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ANSWER 20 only
![18. Find a monic polynomial of least
degree in R[x] that has 4i-1 and -3 as roots.
write the powers of x as x,x^2,x^3,x^4,....
e.g. x^5-2x^4-4x^3+3x^2+2x+1
Enter your answer
19. Find a monic polynomial of least degree in
R[x] that has 1-i and 2i as roots.
write the powers of x as x,x^2,x^3,x^4,.... e.g.
x^5-2x^4-4x^3+3x^2+2x+1
Enter your answer
20. Find the splitting field for x^2-2sqrt(2)x+3
over Q(sqrt(2)). Find the roots first then
simplify.
Note: Q(sqrt(2),u) where u is a root.
Then write the simplest form of this splitting
field.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85584a28-cec6-4119-b265-5692abdcabb3%2Fab53d6c5-409f-449c-b5e3-465551693389%2F87swbui_processed.jpeg&w=3840&q=75)
Transcribed Image Text:18. Find a monic polynomial of least
degree in R[x] that has 4i-1 and -3 as roots.
write the powers of x as x,x^2,x^3,x^4,....
e.g. x^5-2x^4-4x^3+3x^2+2x+1
Enter your answer
19. Find a monic polynomial of least degree in
R[x] that has 1-i and 2i as roots.
write the powers of x as x,x^2,x^3,x^4,.... e.g.
x^5-2x^4-4x^3+3x^2+2x+1
Enter your answer
20. Find the splitting field for x^2-2sqrt(2)x+3
over Q(sqrt(2)). Find the roots first then
simplify.
Note: Q(sqrt(2),u) where u is a root.
Then write the simplest form of this splitting
field.
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