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Question

lf x is real, then (x1)(x3)(x2)(x4) lies in the interval

A
(1,3)
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B
(2,4)
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C
(,)
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D
(3,4)
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Solution

The correct option is C (,)
Let y=(x1)(x3)(x2)(x4)=x24x+3x26x+8
y(x26x+8)=x24x+3
x2(y1)2(3y2)x+(8y3)=0
Since x is real D0
(3y2)2(y1)(8y3)0
9y212y+4(8y211y+3)0y2y+10
Clearly discriminant of quadratic y2y+1 is negative
Hence y2y+1>0 for all y
Therefore y(,)

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