Sequences And Series

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 \(c\)