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

is

3. Show that is contained in and determine that

is irreducible in

4. Determine the Galois group