Chapter 1.2, Problem 68PPSE

Solution

To state: If there are two integers with a product of $-12$ and a sum of $-3$ .

No such pair of two integers is available because the product is negative and both integers have opposite signs.

Given information:

The given statement says to find a pair of integers with a product of $-12$ and a sum of $-3$ .

Explanation:

To get such a pair, find all the possible pairs of two integers whose product is $-12$:

  $\begin{array}{c}-12=12\cdot \left(-1\right)\\ -12=6\cdot \left(-2\right)\\ -12=4\cdot \left(-3\right)\\ -12=3\cdot \left(-4\right)\\ -12=2\cdot \left(-6\right)\\ -12=1\cdot \left(-12\right)\end{array}$

Now add these pairs of integers:

  $\begin{array}{c}12+\left(-1\right)=11\\ 6+\left(-2\right)=4\\ 4+\left(-3\right)=1\\ 3+\left(-4\right)=-1\\ 2+\left(-6\right)=-4\\ 1+\left(-12\right)=-11\end{array}$

It can be seen that there is no such pair of integers whose product is $-12$ and sum is $-3$ .