If `alpha` is an element of an extension field E over a field F, which of the following statements correctly distinguishes between algebraic and transcendental elements over F:
A) `alpha` is algebraic over F if it is a root of any polynomial `p(x) in F[x]`, wheras `alpha` is transcendental over F if it is a root of no non-zero polynomial `p(x) in F[x]`.
B) `alpha` is algebraic over F if it is a root of some non-zero polynomial `p(x) in F[x]`, wheras `alpha` is transcendental over F if it is a root of no non-zero polynomial `p(x) in F[x]` ?