(b)Check whether or not the polynomial- x + 2 e F3lx] is irreducible. Let B be aroot of this polynomial. Is F9 - F3[ß] ?Further, is o : F3[B] → F3[B] given by$(B) = 1 - Bextendtofieldaautomorphism ? Justify your answers.

Check whether or not the polynomial x2 - x + 2 e F3|x] is irreducible. Let ß be a root of this polynomial. Is F9 - F3lß] ? Further, is : F3lß] → F3[B] given by $(B) = 1 - B extend to field %3D a automorphism ? Justify your answers.

Check whether or not the polynomial x2 - x + 2 e F3|x] is irreducible. Let ß be a root of this polynomial. Is F9 - F3lß] ? Further, is : F3lß] → F3[B] given by $(B) = 1 - B extend to field %3D a automorphism ? Justify your answers.

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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Question

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(b)
Check whether or not the polynomial
- x + 2 e F3lx] is irreducible. Let B be a
root of this polynomial. Is F9 - F3[ß] ?
Further, is o : F3[B] → F3[B] given by
$(B) = 1 - B
extend
to
field
a
automorphism ? Justify your answers.

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