Sequence and Series: JEE Main 2024 Mathematics question

For $0 < c < b < a$, let $(a+b-2 c) x^2+(b+c-2 a) x+(c+a-2 b)=0$ 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 $c$