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

1 Answer
Jul 10, 2015

-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