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The set of values of a for which a x^2+(...

The set of values of `a` for which `a x^2+(a-2)x-2` is negative for exactly two integral `x ,` is `(0,2)` b. `[1,2)` c. `(1,2]` d. `(0,2]`

A

`[-1,1]`

B

`[1,2)`

C

`[-1,1]`

D

`[-2,-1])

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` Let `f(x)=ax^(2)+(a-2)x-2`
`f(x)` is negative for two integral values of `x`, so graph should be vertically upward parabola
i.e., `a gt 0`
Let two roots of `f(x)=0` are `alpha` and `beta`, then
`alpha`, `beta=(-a(a-2)+-(a+2))/(2a)`
`impliesa=-1`, `beta=(2)/(a)`
`implies1 lt beta le 2`
`implies 1 lt (2)/(a) le 2`
`implies a in [1,2)`
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