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

Jul 10, 2015

$- 3$ and $- 25$

#### Explanation:

Let the integers be $m$ and $n$ with $\left\mid m \right\mid \le \left\mid n \right\mid$

Since $m n = 75$ 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.

$75 = 3 \cdot 5 \cdot 5$

so $\left(m , n\right)$ must be one of:

$\left(- 1 , - 75\right)$, $\left(- 3 , - 25\right)$, $\left(- 5 , - 15\right)$

Of these only $\left(m , n\right) = \left(- 3 , - 25\right)$ gives us $m + n = - 28$