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x^3-3x^2=0

x^3-3x^2=0 equation

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Numerical solution:

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The solution

You have entered [src] 
 3      2    
x  - 3*x  = 0
x3−3x2=0x^{3} - 3 x^{2} = 0
Simplify
Detail solution
Given the equation:
x3−3x2=0x^{3} - 3 x^{2} = 0
transform
Take common factor x from the equation
we get:
x(x2−3x)=0x \left(x^{2} - 3 x\right) = 0
then:
x1=0x_{1} = 0
and also
we get the equation
x2−3x=0x^{2} - 3 x = 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=−3b = -3
c=0c = 0
, then
D = b^2 - 4 * a * c = 

(-3)^2 - 4 * (1) * (0) = 9

Because D > 0, then the equation has two roots.
x2 = (-b + sqrt(D)) / (2*a)

x3 = (-b - sqrt(D)) / (2*a)

or
x2=3x_{2} = 3
x3=0x_{3} = 0
The final answer for x^3 - 3*x^2 = 0:
x1=0x_{1} = 0
x2=3x_{2} = 3
x3=0x_{3} = 0
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=−3p = -3
q=caq = \frac{c}{a}
q=0q = 0
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=3x_{1} + x_{2} + x_{3} = 3
x1x2+x1x3+x2x3=0x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0
x1x2x3=0x_{1} x_{2} x_{3} = 0
The graph
05-15-10-51015-50005000
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 0
x1=0x_{1} = 0 
x2 = 3
x2=3x_{2} = 3 
x2 = 3
Sum and product of roots [src] 
sum
3
33 
=
3
33 
product
0*3
0⋅30 \cdot 3 
=
0
00 
0
Numerical answer [src] 
x1 = 3.0
x2 = 0.0
x2 = 0.0
The graph
x^3-3x^2=0 equation
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