1. In the following item a field K and a complex number a is given. Find theminimal polynomial of a and the degree of a over K.Oa. K = Q.a =√3+1.b. K=Q, a = √2 + √/2.c. K = Q, a = 1 but a / 1.d. K = Q(√-1), a = √2.e. K = Q(√2), a = √2.f. K = Q, a = 1 but a # 1, p is prime.

According to bartleby guidelines we do only first three subparts and rest part can be reposted…

Answered: 1. In the following item a field K and…

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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1. In the following item a field K and a complex number a is given. Find the minimal polynomial of a and the degree of a over K. O a. K = Q.a = √3+1. b. K=Q, a = √2 + √/2. c. K = Q, a = 1 but a / 1. d. K = Q(√-1), a = √2. e. K = Q(√2), a = √2. f. K = Q, a = 1 but a # 1, p is prime.