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Question

If x is real, then x(x25x+9) lies between

A
1 and 111
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B
1 and 111
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C
1 and 111
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D
none of these
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Solution

The correct option is C 1 and 111
Let,
xx25x+9=y
yx25yx+9y=x
yx2(5y+1)x+9y=0
Now, x is real, so
D0
((5y+1))24y(9y)0
11y2+10y+10
11y210y10
(11y+1)(y1)0
111y1

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