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 - 27 - 4 x - 36 = (18 - 4 x) (x^{2} - 81)

- λ^{3} - 3 λ^{2} + 36 λ + 108 = 0

32 x^{3} + 24 x^{2} + 8 x + 3 = 0

2 x (6 x - 2 x^{2}) + 3 x^{2} (x - 4) = 8

3 z^{6} - j^{2} z^{3} + 8 = 0

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