SOLUTION: I need to know if x^2-9x-10,000=0 can be factored. And what would it be factored into? Thanks, Jennifer

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Question 434657: I need to know if x^2-9x-10,000=0 can be factored. And what would it be factored into?
Thanks,
Jennifer

Found 2 solutions by psbhowmick, solver91311:
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
One word answer: NO
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-9x%2B-10000+=+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=%28-9%29%5E2-4%2A1%2A-10000=40081.

Discriminant d=40081 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--9%2B-sqrt%28+40081+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+40081+%29%29%2F2%5C1+=+104.60119879402
x%5B2%5D+=+%28-%28-9%29-sqrt%28+40081+%29%29%2F2%5C1+=+-95.6011987940204

Quadratic expression 1x%5E2%2B-9x%2B-10000 can be factored:
1x%5E2%2B-9x%2B-10000+=+%28x-104.60119879402%29%2A%28x--95.6011987940204%29
Again, the answer is: 104.60119879402, -95.6011987940204. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-9%2Ax%2B-10000+%29

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Presuming you mean to ask if the trinomial can be factored over the rational numbers, the answer is no.

Consider the discriminant, that is the part of the quadratic formula under the radical, , which is NOT a perfect square. A trinomial is factorable over the rationals if and only if the discriminant is a perfect square.


John

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