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

-3 and -25
Explanation:
Let the integers be m and n with ${\displaystyle \left|m\right|\le \left|n\right|}$
Since ${\displaystyle mn=75}$ is positive, m and n are either both positive or both negative.
If m and n were both positive, then ${\displaystyle m+n}$ would be positive too, but ${\displaystyle m+n=-28}$, so m and n are both negative.
${\displaystyle 75=3\cdot 5\cdot 5}$
so (m, n) must be one of:
${\displaystyle (-1,-75),(-3,-25),(-5,-15)}$
Of these only ${\displaystyle (m,n)=(-3,-25)}$ gives us ${\displaystyle m+n=-28}$.