if you prove one thing you are through ...
all roots of this polynomial are equal (in some appropriate extension)
i'll prove something more than what the problem is asking! i'll show that either is irreducible or for some :
suppose is not irreducible. then for some polynomials where is irreducible with and
differentiating (formally) will give us: hence which is impossible unless and
because so suppose and then and hence letting
we'll get