SOLUTION: FIND THE ZEROS x^2+2x-63=y x^2-x-72=y

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Question 40907: FIND THE ZEROS
x^2+2x-63=y
x^2-x-72=y
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
x^2+2x-63=y
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-63+=+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=%282%29%5E2-4%2A1%2A-63=256.

Discriminant d=256 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+256+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+256+%29%29%2F2%5C1+=+7
x%5B2%5D+=+%28-%282%29-sqrt%28+256+%29%29%2F2%5C1+=+-9

Quadratic expression 1x%5E2%2B2x%2B-63 can be factored:
1x%5E2%2B2x%2B-63+=+1%28x-7%29%2A%28x--9%29
Again, the answer is: 7, -9. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-63+%29

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x^2-x-72=y
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%2B-72+=+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=%28-1%29%5E2-4%2A1%2A-72=289.

Discriminant d=289 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+289+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+289+%29%29%2F2%5C1+=+9
x%5B2%5D+=+%28-%28-1%29-sqrt%28+289+%29%29%2F2%5C1+=+-8

Quadratic expression 1x%5E2%2B-1x%2B-72 can be factored:
1x%5E2%2B-1x%2B-72+=+1%28x-9%29%2A%28x--8%29
Again, the answer is: 9, -8. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B-72+%29

Hope this helps.
Cheers,
Stan H.