SOLUTION: Please help me with this problem. Use a graph, synthetic division, and factoring to find all of the roots of x^3-5x^2+3x=0. Could you show the steps? Thank you so much

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me with this problem. Use a graph, synthetic division, and factoring to find all of the roots of x^3-5x^2+3x=0. Could you show the steps? Thank you so much      Log On


   

Question 28754: Please help me with this problem.
Use a graph, synthetic division, and factoring to find all of the roots of x^3-5x^2+3x=0.
Could you show the steps?
Thank you so much
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Factor out the x to get x(x^2-5x+3)=0
Since x is a factor one solution is x=0
The x^2-5x+3 is a quadratic that is not easily
factored. See the following:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-5x%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=%28-5%29%5E2-4%2A1%2A3=13.

Discriminant d=13 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+13+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+13+%29%29%2F2%5C1+=+4.30277563773199
x%5B2%5D+=+%28-%28-5%29-sqrt%28+13+%29%29%2F2%5C1+=+0.697224362268005

Quadratic expression 1x%5E2%2B-5x%2B3 can be factored:
1x%5E2%2B-5x%2B3+=+1%28x-4.30277563773199%29%2A%28x-0.697224362268005%29
Again, the answer is: 4.30277563773199, 0.697224362268005. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B3+%29

Hope this helps.
Cheers,
Stan H.