What are the solutions to the equation X=X(X-2)^2 ?

The solutions to the equation X=X(X-2)^2 are X=0,X=1,X=3

Find the zeros of X=X(X-2)^2

The zeros of X=X(X-2)^2 are X=0,X=1,X=3

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X = X (X - 2)^{2}

X = 0, X = 1, X = 3

Solution steps

X = X (X - 2)^{2}

Expand

X (X - 2)^{2} : X^{3} - 4 X^{2} + 4 X

X = X^{3} - 4 X^{2} + 4 X

Switch sides

X^{3} - 4 X^{2} + 4 X = X

Move

X

to the left side

X^{3} - 4 X^{2} + 3 X = 0

Factor

X^{3} - 4 X^{2} + 3 X : X (X - 1) (X - 3)

X (X - 1) (X - 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

X = 0 or X - 1 = 0 or X - 3 = 0

Solve

X - 1 = 0 : X = 1

Solve

X - 3 = 0 : X = 3

The solutions are

X = 0, X = 1, X = 3

r^{3} + 3 r^{2} + 3 r + 1 = 0

8 x^{3} - 32 x = 0

x^{3} + 3 x^{2} - 10 x - 24 = 0

7 x^{4} = 7000 x

x^{3} + 4 x^{2} - 7 x - 10 = 0

What are the solutions to the equation X=X(X-2)^2 ?
The solutions to the equation X=X(X-2)^2 are X=0,X=1,X=3
Find the zeros of X=X(X-2)^2
The zeros of X=X(X-2)^2 are X=0,X=1,X=3