1. The polynomail is irreducible in . Find the number if real roots of
2. Let M be the splitting field for over Show that is a Galois extension
and determine its Galois group Is solvable by root?
In the following it can be used without a proof that the Discrimentant of
3. Show that is contained in and determine that
is irreducible in
4. Determine the Galois group