Irreducible Polynomials : No Multiple Roots - Let F be a subfield of C, and let f E F(x) be an irreducible polynomial.
Prove f(x) has no multiple root over C.
Please see the attached file for the fully formatted problem.
Irreducible Polynomial : Splitting Field - Let K be obtained as a field Q(alpha) where alpha is a root of P(x) = x3 −3. Find
an irreducible polynomial which defines the splitting field of P(x).