Question

Please solve this question?

The number of natural numbers for which `(15n^2+8n+6)/n` is a natural number is?

Answer 1

`4`

Explanation:

`(15n^2+8n+6)/n in N`

`15n+8+6/n in N`

We have

`15n+8 in N` for all `n in N`

So we just need to find all `n` for `6/n in N`

In other words,

`n | 6`, or `n` is a factor of `6`, and `n in {1,2,3,6}` (because `6/n > 0`)

There are `4` values for `n` that satisfy the equation `(15n^2+8n+6)/n in N`.

Checking all solutions for `n`:

`n=1, (15n^2+8n+6)/n=29`

`n=2, (15n^2+8n+6)/n=41`

`n=3, (15n^2+8n+6)/n=55`

`n=6, (15n^2+8n+6)/n=99`