To demonstrate the existence of a field with 25 elements, we chose to work with the base field `ZZ_5`. Following the general method, we then needed to find an irreducible polynomial over `ZZ_5`. What specific characteristic must this polynomial posess, according to the method applied in the solution:
A) It must be a polynomial of degree 2 that has no roots in `ZZ_5`.
B) It must be a polynomial of degree 5 that has at least one root in `ZZ_5` ?