SOLUTION: one solution of x^3-5x^2+5x-1=0 is 1. find the other two solutions. if anyone can help me with that problem i would really appreciate them. thank you all again:)

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Question 280378: one solution of x^3-5x^2+5x-1=0 is 1. find the other two solutions.
if anyone can help me with that problem i would really appreciate them. thank you all again:)
Found 2 solutions by checkley77, richwmiller:
Answer by checkley77(12844) (Show Source):
You can put this solution on YOUR website!
Seeing as one of the answers is x=1 then we have:

&&&x^2-4x+1
&&&_________________
(x-1)| x^3-5x^2+5x-1=0
&&& x^3-x^2
&&&&--------
&&&&&-4x^2+5x
&&&&&-4x^2+4x
&&&&&&--------
&&&&&&&+1x-1
&&&&&&&+1x-1
&&&&&&&-----
&&&&&&&&&0
(x-1)(x^2-4x+1)=0
USING THE QUADRATIC EUATION FOR (X^2-4X+1) WE GET:

X=3.732 & X=.268

Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
If x=1 is one solution that means that x-1 is one factor
so you need to divide the equation by (x-1) to get the other factor
to get (x-1) (x^2-4x+1) = 0
now we use the quadratic formula to solve for the other two solutions(roots)
exact forms
x = 2-sqrt(3)
x = 2+sqrt(3)
the approximate forms are given below

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=12 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3.73205080756888, 0.267949192431123. Here's your graph: