If $n^{2} = n + 12$ , then the value of $n .$

n = 6, 2

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n = 3, 4

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n = 12, 1

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n = 4, - 3

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Solution

The correct option is B $n = 4, - 3$
$n^{2} = n + 12$
Transfer the terms to right hand side $n^{2} - n - 12 = 0$
Factorize the equation $n^{2} - n - 12 = 0$ as shown below:
$n^{2} - n - 12 = 0$
$n^{2} - 4 n + 3 n - 12 = 0$
$n (n - 4) + 3 (n - 4) = 0$
$(n - 4) (n + 3) = 0$
$n - 4 = 0$ or $n + 3 = 0$
$n = 4$ or $n = - 3$
Hence the roots of the equation $n^{2} = n + 12$ are $n = - 3, 4$ .

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