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

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Answer 1 · 2015-07-10T23:32:32

$-3$ and $-25$

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 $m + n = -28$

The product of two integers is 7575 and their sum is -28-28. What are the two integers?