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Question

If both the distinct roots of the equation x2axb=0 (a,bR) are lying in between 2 and 2, then

A
|a|<2b2
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B
|a|>2b2
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C
|a|<4
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D
|a|>b22
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Solution

The correct option is D |a|>b22

Required conditions are
(1) f(2)>0,(2) f(2)>0,(3) 2<B2A<2,(4) D>0

f(2)>0
4+2ab>0
a>b22
(2b2)<a ...(i)

f(2)>0
42ab>0
a<2b2 ...(ii)

From (i) and (ii),
(2b2)<a<2b2
|a|<2b2

Since, |a|0
2b2>0
b22<0|a|
|a|>b22

2<B2A<2
2<a2<2
4<a<4
a(4,4)
|a|<4


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