The set of values of a for which ax2+(a−2)x−2 is negative for exactly two integral values of x, is
A
(0,2)
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B
[1,2)
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C
(1,2]
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D
(0,2]
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Solution
The correct option is B[1,2) f(x)=ax2+(a−2)x−2 Let f(x)=0 Roots of the above equations are −1 and 2a ∵f(0)=−2<0 ∴ For the above expression to be negative only for two integers then a>0,
1st integer is 0 so second integer must be 1
which implies the second root must >1 and ≤2 ⇒1<2a≤2 ⇒1≤a<2 ∴a∈[1,2).