In the finite field `ZZ_2(alpha)`, where `alpha` is a root of the irreducible polynomial
`x^3 + x^2 + 1` over `ZZ_2` ,
consider the polynomial
`p(x) = x^2 + (1 + alpha)x + (alpha^2 + alpha)`.
Which of the following statements is true:
A) The polynomial has exactly one root in `ZZ_2(alpha)`, and it is `alpha^2`.
B) The polynomial has exactly two distinct roots in `ZZ_2(alpha)`, and they are `alpha^2` and `alpha^4`. ?