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x³-2x²+x=0 equation

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Numerical solution:

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The solution

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 3      2        
x  - 2*x  + x = 0
x+(x3−2x2)=0x + \left(x^{3} - 2 x^{2}\right) = 0
Simplify
Detail solution
Given the equation:
x+(x3−2x2)=0x + \left(x^{3} - 2 x^{2}\right) = 0
transform
Take common factor x from the equation
we get:
x(x2−2x+1)=0x \left(x^{2} - 2 x + 1\right) = 0
then:
x1=0x_{1} = 0
and also
we get the equation
x2−2x+1=0x^{2} - 2 x + 1 = 0
This equation is of the form
a*x^2 + b*x + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
x2=D−b2ax_{2} = \frac{\sqrt{D} - b}{2 a}
x3=−D−b2ax_{3} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=1a = 1
b=−2b = -2
c=1c = 1
, then
D = b^2 - 4 * a * c = 

(-2)^2 - 4 * (1) * (1) = 0

Because D = 0, then the equation has one root.
x = -b/2a = --2/2/(1)

x2=1x_{2} = 1
The final answer for x^3 - 2*x^2 + x = 0:
x1=0x_{1} = 0
x2=1x_{2} = 1
Vieta's Theorem
it is reduced cubic equation
px2+qx+v+x3=0p x^{2} + q x + v + x^{3} = 0
where
p=bap = \frac{b}{a}
p=−2p = -2
q=caq = \frac{c}{a}
q=1q = 1
v=dav = \frac{d}{a}
v=0v = 0
Vieta Formulas
x1+x2+x3=−px_{1} + x_{2} + x_{3} = - p
x1x2+x1x3+x2x3=qx_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q
x1x2x3=vx_{1} x_{2} x_{3} = v
x1+x2+x3=2x_{1} + x_{2} + x_{3} = 2
x1x2+x1x3+x2x3=1x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 1
x1x2x3=0x_{1} x_{2} x_{3} = 0
The graph
-15.0-12.5-10.0-7.5-5.0-2.50.02.55.07.510.012.515.0-25002500
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 0
x1=0x_{1} = 0 
x2 = 1
x2=1x_{2} = 1 
x2 = 1
Sum and product of roots [src] 
sum
1
11 
=
1
11 
product
0
00 
=
0
00 
0
Numerical answer [src] 
x1 = 0.0
x2 = 1.0
x2 = 1.0
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