SOLUTION: The sum of two numbers is 8 and the product is -12 what are the numbers?

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Question 1097620: The sum of two numbers is 8 and the product is -12 what are the numbers?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of two numbers is 8 and the product is -12 what are the numbers?
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x + y = 8 --> y = -x+8
x*y = -12
Sub for y
x*(-x+8) = -12
x^2 - 8x - 12 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-8x%2B-12+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-8%29%5E2-4%2A1%2A-12=112.

Discriminant d=112 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+112+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+112+%29%29%2F2%5C1+=+9.29150262212918
x%5B2%5D+=+%28-%28-8%29-sqrt%28+112+%29%29%2F2%5C1+=+-1.29150262212918

Quadratic expression 1x%5E2%2B-8x%2B-12 can be factored:
1x%5E2%2B-8x%2B-12+=+%28x-9.29150262212918%29%2A%28x--1.29150262212918%29
Again, the answer is: 9.29150262212918, -1.29150262212918. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-8%2Ax%2B-12+%29