Let `alpha` be an element algebraic over a field F, and let `irr(alpha , F)` denote the minimal polynomial of `alpha` over F. If `irr(alpha , F)` has degree 4, which of the following statements is true:
A) The field extension `F(alpha)"/"F` contains exactly four distinct elements.
B) The field extension `F(alpha)"/"F` has dimension 4 over F, meaning every element in `F(alpha)` can be expressed as a linear combination of `1 , alpha , alpha^2 , alpha^3` with coefficients in F ?