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?