In the proof that `beta` is algebraic over `F(alpha)`, why must at least one coefficient `b_j(alpha)` in the polynomial equation `sum_(j = 0)^m b_j(alpha)beta^j = 0` be non-zero:
A) If all `b_(alpha) = 0`, this would imply a non-trivial polynomial equation for `alpha` over F, contradicting `alpha's` transcendence.
B) If all `b_j(alpha) = 0`, the equation reduces to 0 = 0, making `beta` algebraic ?