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Question

If x is real, then the value of the expression x2+14x+9x2+2x+3 lies between

A
4 and 5
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B
4 and 5
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C
5 and 4
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D
None of these
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Solution

The correct option is C 5 and 4
Let y=x2+14x+9x2+2x+3
x2+14x+9=x2y+2xy+3y
x2(y1)+2x(y7)+(3y9)=0
Since, x is real, we have
4(y7)24(3y9)(y1)>0
(y2+4914y)(3y2+912y)>0
(y+5)(y4)<0
Therefore, y lies between 5 and 4.

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