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

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) (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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=13 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 4.30277563773199, 0.697224362268005. Here's your graph:

Hope this helps.
Cheers,
Stan H.
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