Operating on consecutive integers

Doing more than addition to consecutive integers 

The Problem The product of two consecutive integers is 20. What are the integers  

Write the two consecutive integers as n and n + 1. Multiply them together and set the equation equal to 20. You get a quadratic equation that s solved by setting the equation equal to 0, factoring, and solving for the numbers. 

The quadratic equation gives you two different answers. When n = 4, you get the two consecutive integers 4 and 5. The product of 4 and 5 is, indeed, 20. But what about the solution n = -5 If n = -5, then n+l=-5+l = -4. The product of -5 and -4 is also 20. This problem has two different solutions. As long as you re happy with negative integers, too, then you accept both sets of answers. 

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