What are the solutions to the equation y^4-y=0 ?

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

Find the zeros of y^4-y=0

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

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y^{4} - y = 0

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

Solution steps

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

3 x^{3} + 2 x^{2} - 27 x - 18 = 0

(3 - x) (x^{2} + 15) = 0

x^{3} + 6 x^{2} - 36 x - 216 = 0

m^{3} = 343

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

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