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)$\quad$ If $\alpha \in (-1, 0)$, then $b$ cannot be the geometric mean of $a$ and $c$
(II)$\quad$ If $\alpha \in (0, 1)$, then $b$ may be the geometric mean of $a$ and $c$
