SOLUTION: solve using the quadratic formula. express answers as exact roots. x^2-6x+3=0 3x^2+5x+1=0 3x^2-6x-8=0 4x^2-2x+5=0 b^2+3b=1

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: solve using the quadratic formula. express answers as exact roots. x^2-6x+3=0 3x^2+5x+1=0 3x^2-6x-8=0 4x^2-2x+5=0 b^2+3b=1      Log On


   

Question 876091: solve using the quadratic formula. express answers as exact roots.
x^2-6x+3=0
3x^2+5x+1=0
3x^2-6x-8=0
4x^2-2x+5=0
b^2+3b=1
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
solve using the quadratic formula. express answers as exact roots.
x^2-6x+3=0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-6x%2B3+=+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=%28-6%29%5E2-4%2A1%2A3=24.

Discriminant d=24 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+24+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+24+%29%29%2F2%5C1+=+5.44948974278318
x%5B2%5D+=+%28-%28-6%29-sqrt%28+24+%29%29%2F2%5C1+=+0.550510257216822

Quadratic expression 1x%5E2%2B-6x%2B3 can be factored:
1x%5E2%2B-6x%2B3+=+%28x-5.44948974278318%29%2A%28x-0.550510257216822%29
Again, the answer is: 5.44948974278318, 0.550510257216822. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B3+%29

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The others are similar.
3x^2+5x+1=0
3x^2-6x-8=0
4x^2-2x+5=0
b^2+3b=1