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

Options

A. (0,2)
B. [1,2)
C. (1, 2]
D. (0,2]

Answer

2

Explanation

`f(x) = ax^(2) + (a - 2) x - 2 = (ax - 2 )(x + 1)`
`f(0) = - 2 and f(-1) = 0`
If a is negative then expression
becomes negative for intinite vales
of x, therefore it must be positive
Expression to be negative for exactly
two integral values of x
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So `(2)/(a) le 2 or a ge 1`
and ` (2)/(a) gt 1 rArr a lt 2`
`therefore a in [ 1, 2)`