## Splitting fields

Hi.Let f and g be irreducible polynomials with deg(f)=deg(g)=3 over a field K, which is a subset of the real numbers.Let the discriminant of f be positive and the discriminant of g be negative.Define Z_f :=splitting field of f and Z_g :=splitting field of g. Now my Question: Why is the intersection of Z_f and Z_g the field K ?Thanks in advance,Bye,Alexander