SOLUTION: Use the quadratic formula to find the roots of 3x^2+10x-5=0

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Question 179924: Use the quadratic formula to find the roots of 3x^2+10x-5=0
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
3x^2+10x-5=0
:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B10x%2B-5+=+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=%2810%29%5E2-4%2A3%2A-5=160.

Discriminant d=160 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-10%2B-sqrt%28+160+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2810%29%2Bsqrt%28+160+%29%29%2F2%5C3+=+0.441518440112253
x%5B2%5D+=+%28-%2810%29-sqrt%28+160+%29%29%2F2%5C3+=+-3.77485177344559

Quadratic expression 3x%5E2%2B10x%2B-5 can be factored:
3x%5E2%2B10x%2B-5+=+%28x-0.441518440112253%29%2A%28x--3.77485177344559%29
Again, the answer is: 0.441518440112253, -3.77485177344559. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B10%2Ax%2B-5+%29