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If 2a, b, 2c are in A.P. where a, b, c a...

If `2a`, `b`, `2c` are in `A.P.` where `a`, `b`, `c` are `R^(+)`, then the expression `f(x)=(ax^(2)-bx+c)` has

A

both roots negative

B

both roots positive

C

atleast one root between `0` and `2`

D

roots are of opposite sign.

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` Since `2a`, `b`, `2c` are in `A.P.`, therefore
`2a+2c=2b`
`impliesa-b+c=0`
`:.f(1)=0`
Also `f(0)= c gt 0`
Therefore, product of roots is positive.
Therefore, other root is also positive.
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