SOLUTION: CAN YOU HELP ME FIND TWO NUMBERS WHOSE PRODUCT IS 20 AND SUM IS 17

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Question 774514: CAN YOU HELP ME FIND TWO NUMBERS WHOSE PRODUCT IS 20 AND SUM IS 17
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
CAN YOU HELP ME FIND TWO NUMBERS WHOSE PRODUCT IS 20 AND SUM IS 17
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Try pairs of factors of 20
1*20
2*10
4*5
Only 3 integer possibilities, and none have a sum of 17.
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x*(17-x) = 20
x%5E2+-+17x+%2B+20+=+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-17x%2B20+=+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=%28-17%29%5E2-4%2A1%2A20=209.

Discriminant d=209 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--17%2B-sqrt%28+209+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-17%29%2Bsqrt%28+209+%29%29%2F2%5C1+=+15.7284161474005
x%5B2%5D+=+%28-%28-17%29-sqrt%28+209+%29%29%2F2%5C1+=+1.27158385259952

Quadratic expression 1x%5E2%2B-17x%2B20 can be factored:
1x%5E2%2B-17x%2B20+=+%28x-15.7284161474005%29%2A%28x-1.27158385259952%29
Again, the answer is: 15.7284161474005, 1.27158385259952. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-17%2Ax%2B20+%29

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