SOLUTION: Find the x intercepts of f(x) = 3x^2 -15x -13

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Question 392412: Find the x intercepts of
f(x) = 3x^2 -15x -13
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = 3x^2 -15x -13
set f(x) to zero and solve for x:
0 = 3x^2 -15x -13
applying the "quadratic formula" we get:
x = {5.753, -0.753}
.
Details of quadratic follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-15x%2B-13+=+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=%28-15%29%5E2-4%2A3%2A-13=381.

Discriminant d=381 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--15%2B-sqrt%28+381+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-15%29%2Bsqrt%28+381+%29%29%2F2%5C3+=+5.75320354932386
x%5B2%5D+=+%28-%28-15%29-sqrt%28+381+%29%29%2F2%5C3+=+-0.753203549323856

Quadratic expression 3x%5E2%2B-15x%2B-13 can be factored:
3x%5E2%2B-15x%2B-13+=+3%28x-5.75320354932386%29%2A%28x--0.753203549323856%29
Again, the answer is: 5.75320354932386, -0.753203549323856. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-15%2Ax%2B-13+%29