For $$0 \lt c \lt b \lt a$$, let $$(a + b - 2c)x^2 + (b + c - 2a)x + (c + a - 2b) = 0$$ and $$\alpha \neq 1$$ be one of its root. Then, among the two statements (I) If $$\alpha \in (-1, 0)$$, then $$b$$ cannot be the geometric mean of $$a$$ and $$c$$. (II) If $$\alpha \in (0, 1)$$, then $$b$$ may be the geometric mean of $$a$$ and $$c$$.

A

Both (I) and (II) are true

B

Neither (I) nor (II) is true

C

Only (II) is true

D

Only (I) is true