What are the solutions to the equation x-x^9=0 ?

The solutions to the equation x-x^9=0 are

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x-x^9=0

x - x^{9} = 0

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

Solution steps

x - x^{9} = 0

Factor

x - x^{9} : - x (x^{2} + 2 x + 1) (x^{2} - 2 x + 1) (x^{2} + 1) (x + 1) (x - 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Solve

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

Solve

x^{2} + 1 = 0 : x = i, x = - i

Solve

x + 1 = 0 : x = - 1

Solve

x - 1 = 0 : x = 1

The solutions are

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

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

x^{4} - 2 x^{3} + 2 x^{2} - 8 x - 8 = 0

x^{4} - 6 x^{2} - 8 x - 3 = 0

λ^{3} - 2 λ^{2} - 5 λ + 6 = 0

(4 b)^{4} = 2 b

What are the solutions to the equation x-x^9=0 ?
The solutions to the equation x-x^9=0 are
Find the zeros of x-x^9=0
The zeros of x-x^9=0 are