Question

In: Advanced Math

Question 1: a) What are the complex roots of x^8-1 ? b) What are the irreducible...

Question 1:

a) What are the complex roots of x^8-1 ?

b) What are the irreducible factors of f(x)=x^8-1 in R[x]?

c) What are the irreducible factors of f(x)=x^8-1 in Q[x]?

Expert Solution

(a) We have to find out complex root of

now

......................................(1)

Thus we have

also,

Again we have

where n be integer

so we have n=0,1,2,3

when n=0 then

When n=1

when n=2

when n=3

Hence we got the complex root are

and

(b) Form (1) we seen that so the irreducable factor of in is and

(c) Here also irreduciable factor of in is and

Colby Messinger answered 2 years ago

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