What are the solutions to the equation 0=x^4-4x^3+4x^2-x ?

The solutions to the equation 0=x^4-4x^3+4x^2-x are x=0,x=1,x=(3+sqrt(5))/2 ,x=(3-sqrt(5))/2

Find the zeros of 0=x^4-4x^3+4x^2-x

The zeros of 0=x^4-4x^3+4x^2-x are x=0,x=1,x=(3+sqrt(5))/2 ,x=(3-sqrt(5))/2

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

x = 0, x = 1, x = \frac{3 + 5}{2}, x = \frac{3 - 5}{2}

Decimal Notation

x = 0, x = 1, x = 2.61803 \dots, x = 0.38196 \dots

Solution steps

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

Switch sides

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

Factor

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

x (x - 1) (x^{2} - 3 x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 1 = 0 or x^{2} - 3 x + 1 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{2} - 3 x + 1 = 0 : x = \frac{3 + 5}{2}, x = \frac{3 - 5}{2}

The solutions are

x = 0, x = 1, x = \frac{3 + 5}{2}, x = \frac{3 - 5}{2}

786000 = 247000 e^{17}

60 x - 3 x^{2} - 3 x^{3} = 0

x^{3} + x - 56 = 0

16 k^{4} = 1296

288 = 24 x^{12}

What are the solutions to the equation 0=x^4-4x^3+4x^2-x ?
The solutions to the equation 0=x^4-4x^3+4x^2-x are x=0,x=1,x=(3+sqrt(5))/2 ,x=(3-sqrt(5))/2
Find the zeros of 0=x^4-4x^3+4x^2-x
The zeros of 0=x^4-4x^3+4x^2-x are x=0,x=1,x=(3+sqrt(5))/2 ,x=(3-sqrt(5))/2