Question

The product of two integers is `75` and their sum is `-28`. What are the two integers?

Answer 1

`-3` and `-25`

Explanation:

Let the integers be `m` and `n` with `abs(m) <= abs(n)`

Since `mn = 75` is positive, `m` and `n` are either both positive or both negative.

If `m` and `n` were both positive, then `m + n` would be positive too, but `m + n = -28`, so `m` and `n` are both negative.

`75 = 3 * 5 * 5`

so `(m, n)` must be one of:

`(-1, -75)`, `(-3, -25)`, `(-5, -15)`

Of these only `(m, n) = (-3, -25)` gives us `m + n = -28`