Let [ ] represents the greatest integer function and $[x^{3} + x^{2} + 1 + x] = [x^{3} + x^{2} + 1] + x .$ The number of solution(s) of the equation in $| [x] | = 2 - | [x] |$ is

1

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Z e r o

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3

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2

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Solution

The correct option is B $2$
Given that,
$[x^{3} + x^{2} + 1 + x] = [x^{3} + x^{2} + 1] + x$

Possible when $x^{3} + x^{2} + 1$ and $x$ are in sequence .
no. of solution of the equation.

$\begin{matrix} | [x] | = 2 - | [x] | 2 | [x] | = 2 | [x] | = 1 [x] = \pm 1 [x] = 1 [x] = - 1 \end{matrix}$

Therefore,
Number of solution $= 2$

Hence, this is the answer.

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