All the values of `' a '` for which the quadratic expression `a x^2+(a-2)x-2` is negative for exactly two integral values of `x` may lie in (a) `[1,3/2]` (b) `[3/2,2)` (c) `[1,2)` (d) `[-1,2)`

Options

A. `[-1,1]`
B. `[1,2)`
C. `[-1,1]`
D. `[-2,-1])

Answer

B

Explanation

`(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-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)`