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Question

The set of values of a for which ax2+(a2)x2 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+(a2)x2
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<2a2
1a<2
a[1,2).

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