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Question

If x is real and x23x+2>0,x23x40, then which one of the following is correct ?

A
1x4
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B
2x4
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C
1<x1
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D
1x<1 or 2<x4
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Solution

The correct option is D 1x<1 or 2<x4
Consider first : x23x+2>0
(x1)(x2)>0
x<1 or x>2 ...(1)
And x23x40
(x4)(x+1)0
1x4 ...(2)
Combining (1) and (2)
1x<1 or 2<x4
Drawing on number line :

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