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Question

The number of integral values of b for which the origin and the point (1,1) lie on the same side of the straight line a2x+aby+1=0,for all aR{0} is

A
1
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B
3
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C
2
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D
5
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Solution

The correct option is B 3
For same side of a2x+aby+1=0 of origin & (1,1).
1×a2+ab+11>0
Given, aR{0}
Then,
a2+ab+1>0
This must be true for all values of a except 0.
Hence,
Δ>0 and coefficient of a2 must be positive.
b24<0
|b|<2
The integral values which b can take are 1,0,1

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