surgrimpig3x

2022-02-05

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

deliria1t4

Beginner2022-02-06Added 13 answers

-3 and -25

Explanation:

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

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.

$75=3\cdot 5\cdot 5$

so (m, n) must be one of:

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

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

Explanation:

Let the integers be m and n with

Since

If m and n were both positive, then

so (m, n) must be one of:

Of these only