Mathematics

Problem

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

(A) Both (I) and (II) are true (B) Neither (I) nor (II) is true (C) Only (II) is true (D) Only (I) is true