SOLUTION: Which of the following is one of the two biomial factors of 6s^2+40s-64?

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Question 5531: Which of the following is one of the two biomial factors of 6s^2+40s-64?
Answer by Abbey(339) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B40x%2B-647+=+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=%2840%29%5E2-4%2A6%2A-647=17128.

Discriminant d=17128 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-40%2B-sqrt%28+17128+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2840%29%2Bsqrt%28+17128+%29%29%2F2%5C6+=+7.57283209932192
x%5B2%5D+=+%28-%2840%29-sqrt%28+17128+%29%29%2F2%5C6+=+-14.2394987659886

Quadratic expression 6x%5E2%2B40x%2B-647 can be factored:
6x%5E2%2B40x%2B-647+=+6%28x-7.57283209932192%29%2A%28x--14.2394987659886%29
Again, the answer is: 7.57283209932192, -14.2394987659886. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B40%2Ax%2B-647+%29