What are the solutions to the equation y=y^4 ?

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

Find the zeros of y=y^4

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

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y = y^{4}

y = 0, y = 1, y = - \frac{1}{2} + \frac{3}{2} i, y = - \frac{1}{2} - \frac{3}{2} i

Solution steps

y = y^{4}

Switch sides

y^{4} = y

Move

y

to the left side

y^{4} - y = 0

Factor

y^{4} - y : y (y^{3} - 1)

y (y^{3} - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y = 0 or y^{3} - 1 = 0

Solve

y^{3} - 1 = 0 : y = 1, y = - \frac{1}{2} + \frac{3}{2} i, y = - \frac{1}{2} - \frac{3}{2} i

The solutions are

y = 0, y = 1, y = - \frac{1}{2} + \frac{3}{2} i, y = - \frac{1}{2} - \frac{3}{2} i

x, x^{3} - x = 0

x^{3} - 12 = 0

2 x^{3} + x = 0

x^{4} - 6 x^{2} - 27 = 0

x^{4} + 2 x + 1 = 0

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