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

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

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

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

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

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

Decimal Notation

x = 0, x = 0.61803 \dots, x = - 1.61803 \dots

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

The solutions are

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

z^{3} = 1 - i

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

y^{3} + 8 = 0

(x^{2} - 4)^{2} = 0

- 3 \cdot 4 + 25 = - 5 + x^{6}

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