Consecutive integers quadratic equations

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. 

The product of the two consecutive odd integers is written as rt(n + 2). Set that product equal to 143, set the equation equal to 0, and solve the quadratic equation that results. 

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