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Question

Number of integral solutions of [x+2][x2+1]>12 is / are


A

0

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B

1

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C

2

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D

3

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E

4

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Solution

The correct option is D

3


Explanation for the correct option:

Finding the number of integral solutions of [x+2][x2+1]>12

Given: [x+2][x2+1]>12

Solving [x+2][x2+1]>12 to find the values of x

[x+2][x2+1]>12⇒2x+4>x2+1⇒x2–2x–3<0⇒(x–3)(x+1)<0⇒–1<x<3

The integral solution is 3

∴The value of x is 0,1,2.

Hence the correct answer is option (D)


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