If \( a, b \) and \( c \) are positive numbers such that \( abc \) and the equation \( (a+b-2 c)...

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If \( a, b \) and \( c \) are positive numbers such that \( abc \) and the equation \( (a+b-2 c) x^{2}+(b+c-2 a) x+(c+a-2 b) \) \( =0 \) has a root in the interval \( (-1,0) \), then
(A) \( b \) cannot be the G.M. of \( a, c \)
(B) \( b \) may be the G.M. of \( a, c \)
(C) \( b \) is the G.M. of \( a, c \)
(D) none of these
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