For $0 < c < b < a$, let $(a+b-2c)x^{2} + (b+c-2a)x + (c+a-2b) = 0$ and let $\alpha \ne 1$ be one of its roots. 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 $c$.