SOLUTION: What are the solutions to the quadratic function: 3x^2-11x-4=0.

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Question 444648: What are the solutions to the quadratic function: 3x^2-11x-4=0.
Answer by chriswen(106) 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 3x%5E2%2B-11x%2B-4+=+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=%28-11%29%5E2-4%2A3%2A-4=169.

Discriminant d=169 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--11%2B-sqrt%28+169+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-11%29%2Bsqrt%28+169+%29%29%2F2%5C3+=+4
x%5B2%5D+=+%28-%28-11%29-sqrt%28+169+%29%29%2F2%5C3+=+-0.333333333333333

Quadratic expression 3x%5E2%2B-11x%2B-4 can be factored:
3x%5E2%2B-11x%2B-4+=+3%28x-4%29%2A%28x--0.333333333333333%29
Again, the answer is: 4, -0.333333333333333. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-11%2Ax%2B-4+%29