For $0 < c < b < a$, 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 $c$.