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Question

If $A equals open curly brackets n colon fraction numerator n to the power of 3 end exponent plus 5 n to the power of 2 end exponent plus 2 over denominator n end fraction blank i s blank a n blank i n t e g e r blank a n d blank i t s e l f blank i s blank a n blank i n t e g e r close curly brackets comma$ then the number of elements in the set $A comma$ is

1
2
3
4

The correct answer is: 4

We have,
$fraction numerator n to the power of 3 end exponent plus 5 n to the power of 2 end exponent plus 2 over denominator n end fraction equals n to the power of 2 end exponent plus 5 n plus fraction numerator 2 over denominator n end fraction$
$therefore fraction numerator n to the power of 3 end exponent plus 5 n to the power of 2 end exponent plus 2 over denominator n end fraction$ is an integer, if $fraction numerator 2 over denominator n end fraction$ is an integer
$rightwards double arrow n equals plus-or-minus 1 comma plus-or-minus 2$
$rightwards double arrow$ A consists of four elements $v i z. negative 1 comma blank 1 comma negative 2 comma blank 2$

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