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If a, b, c are positive numbers such tha...

If `a`, `b`, `c` are positive numbers such that `a gt b gt c` and the equation `(a+b-2c)x^(2)+(b+c-2a)x+(c+a-2b)=0` has a root in the interval `(-1,0)`, then

A

`a+c lt 2b`

B

both roots are rational

C

`ax ^(2) +2bx+c=0` have both roots negative

D

`cx ^(2)+2bx+a=0` have both roots negative

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