SOLUTION: 4x^3-27x^2-11x-1=0

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Question 254984: 4x^3-27x^2-11x-1=0
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
factor it
(4x+1)*(x^2-7x-1) = 0
three solutions
4x+1=0 solve for x
x^2-7x-1=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-7x%2B1+=+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=%28-7%29%5E2-4%2A1%2A1=45.

Discriminant d=45 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--7%2B-sqrt%28+45+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+45+%29%29%2F2%5C1+=+6.85410196624968
x%5B2%5D+=+%28-%28-7%29-sqrt%28+45+%29%29%2F2%5C1+=+0.145898033750315

Quadratic expression 1x%5E2%2B-7x%2B1 can be factored:
1x%5E2%2B-7x%2B1+=+1%28x-6.85410196624968%29%2A%28x-0.145898033750315%29
Again, the answer is: 6.85410196624968, 0.145898033750315. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-7%2Ax%2B1+%29