For which fields Fand polynomials fE F[X]), described below, does the quotient ring F[X]/(F[X] f) consist of 64 elements? O F has characteristic 2 and degree 3 over its prime subfield, f e F[X] has degree 3. cross out O P has characteristic 3 and degree 2 over its prime subfield, f e F[X] has degree 2. cross out O F has characteristic 2 and degree 3 over its prime subfield, f e F[X] has degree 2. cross out O F has characteristic 2 and degree 2 over its prime subfield, f e F[X] has degree 3. cross out
For which fields Fand polynomials fE F[X]), described below, does the quotient ring F[X]/(F[X] f) consist of 64 elements? O F has characteristic 2 and degree 3 over its prime subfield, f e F[X] has degree 3. cross out O P has characteristic 3 and degree 2 over its prime subfield, f e F[X] has degree 2. cross out O F has characteristic 2 and degree 3 over its prime subfield, f e F[X] has degree 2. cross out O F has characteristic 2 and degree 2 over its prime subfield, f e F[X] has degree 3. cross out
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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Solve the given question in 20 min plz q2
![For which fields F and polynomials f E F[X]), described below, does the quotient ring F[X]/(F[X] ) consist of 64
elements?
O F has characteristic 2 and degree 3 over its prime
subfield, f e F[X] has degree 3.
cross out
O F has characteristic 3 and degree 2 over its prime
subfield, f e F[X] has degree 2.
cross out
O F has characteristic 2 and degree 3 over its prime
subfield, f e F[X] has degree 2.
cross out
O F has characteristic 2 and degree 2 over its prime
subfield, f e F[X] has degree 3.
cross out](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65b1e2d8-714f-4bbb-980a-647457c3e45f%2F44073955-f5f0-4244-a8ff-c454625ce382%2Fy8q4ni_processed.jpeg&w=3840&q=75)
Transcribed Image Text:For which fields F and polynomials f E F[X]), described below, does the quotient ring F[X]/(F[X] ) consist of 64
elements?
O F has characteristic 2 and degree 3 over its prime
subfield, f e F[X] has degree 3.
cross out
O F has characteristic 3 and degree 2 over its prime
subfield, f e F[X] has degree 2.
cross out
O F has characteristic 2 and degree 3 over its prime
subfield, f e F[X] has degree 2.
cross out
O F has characteristic 2 and degree 2 over its prime
subfield, f e F[X] has degree 3.
cross out
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