SOLUTION: G(x)=3x^2-4x-1

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Question 923905: G(x)=3x^2-4x-1
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Thx for letting us know.
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If you want to find the zeroes:
3x^2-4x-1 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-4x%2B-1+=+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=%28-4%29%5E2-4%2A3%2A-1=28.

Discriminant d=28 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+28+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+28+%29%29%2F2%5C3+=+1.54858377035486
x%5B2%5D+=+%28-%28-4%29-sqrt%28+28+%29%29%2F2%5C3+=+-0.21525043702153

Quadratic expression 3x%5E2%2B-4x%2B-1 can be factored:
3x%5E2%2B-4x%2B-1+=+%28x-1.54858377035486%29%2A%28x--0.21525043702153%29
Again, the answer is: 1.54858377035486, -0.21525043702153. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-4%2Ax%2B-1+%29

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