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

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

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y-y^9=0

y - y^{9} = 0

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

Solution steps

y - y^{9} = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Solve

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

Solve

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

Solve

y + 1 = 0 : y = - 1

Solve

y - 1 = 0 : y = 1

The solutions are

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

x^{4} - 48 x^{2} + 512 = 0

(2 x - 3) (x^{2} - 16) = 0

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

x^{6} - 13 x^{3} + 42 = 0

x^{7} = 0

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