SOLUTION: the sum of two integers is-33 and their product is 162.develop a quadratic equation and then solve to find the value of the two intergers.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: the sum of two integers is-33 and their product is 162.develop a quadratic equation and then solve to find the value of the two intergers.      Log On


   

Question 1143566: the sum of two integers is-33 and their product is 162.develop a quadratic equation and then solve to find the value of the two intergers.
Answer by greenestamps(13208) About Me  (Show Source):
You can put this solution on YOUR website!


Since the sum of the two integers is -33, let the two integers be x and (-33-x).

Then, since their product is 162,

x%28-33-x%29+=+162
-33x-x%5E2+=+162
x%5E2%2B33x%2B162+=+0
%28x%2B27%29%28x%2B6%29+=+0

The two integers are -27 and -6.

Note that in solving the quadratic equation by factoring, you had to find two numbers whose sum is 33 and whose product is 162.

Except for the signs of the integers, that is basically what the original problem asked you to do. So the formal algebra wasn't really any help.

The quickest and easiest way to solve the problem is first to notice that since the sum is negative and the product is positive, both integers have to be negative. Then ignore the signs and look for a pair of numbers with a product of 162 that has a sum of 33.