SOLUTION: What are 2 numbers that add together to get -23 and multiply to get -120

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Question 891597: What are 2 numbers that add together to get -23 and multiply to get -120
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What are 2 numbers that add together to get -23 and multiply to get -120
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x + y = -23
x*y = -120 --> y = -120/x
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x - (120/x) = -23
x%5E2+-+120+=+-23x
x%5E2+%2B+23x+-+120+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B23x%2B-120+=+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=%2823%29%5E2-4%2A1%2A-120=1009.

Discriminant d=1009 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-23%2B-sqrt%28+1009+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2823%29%2Bsqrt%28+1009+%29%29%2F2%5C1+=+4.38238017426859
x%5B2%5D+=+%28-%2823%29-sqrt%28+1009+%29%29%2F2%5C1+=+-27.3823801742686

Quadratic expression 1x%5E2%2B23x%2B-120 can be factored:
1x%5E2%2B23x%2B-120+=+%28x-4.38238017426859%29%2A%28x--27.3823801742686%29
Again, the answer is: 4.38238017426859, -27.3823801742686. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B23%2Ax%2B-120+%29