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Trying to do i) and iii) on this past exam paper

For part i) I'm pretty stumped

I've said that the possible roots of the polynomial are +- all the factors of T

In particular rt(T) needs to be a factor of T but this can't be possible?

Doesn't sound too good but its the best I've got.

Part iii) I know this means that every element in K is seperable over k, i.e that the minimal polynomials of elements in K are seperable, where they have no repeated roots.

Not sure how to apply this though..

Maybe K = k(rt(T))

so the minimal polynomial of K is X^2 - T which has repeated root rt(T) so it is inseperable?

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# Homework Help: Irreducibility and finite fields

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