Question

P= (78n2 + 96n + 576)/n, where P is an integer. How many values of "n" satisfy this condition?
A 8
B). 11
C
12
D24​

Answer 1

Given info : P = (78n² + 96n + 576)/n , where P is an integer.

To find : no of values of n satisfying the above condition is...

solution : P = (78n² + 96n + 576)/n

⇒P = 78n + 96 + 576/n

it is clear that, P will be integer only when 576/n is an integer.

576/n = integers when n is prime factors of 576.

576 = 2⁶ × 3²

I.e., no of factors = (6 + 1)(2 + 1) = 7 × 3 = 21

Therefore the no of values of n is 21.

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