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If a,b,c are rational numbers (a gt b gt...

If a,b,c are rational numbers `(a gt b gt c gt 0)` and quadratic equation `(a+b-2x) x ^(2) + (b+c-2a) x+ (c+a-2b)=0` has a root in the interval `(-1,0)` then which of the following statement (s) is/are correct ?

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

Text Solution

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The correct Answer is:
A, B, C, D
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