What are the solutions to the equation y^6-3y^4+3y^2-y=0 ?

The solutions to the equation y^6-3y^4+3y^2-y=0 are y=0,y=1,y\approx 1.28879…,y\approx 0.38939…

Find the zeros of y^6-3y^4+3y^2-y=0

The zeros of y^6-3y^4+3y^2-y=0 are y=0,y=1,y\approx 1.28879…,y\approx 0.38939…

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y^{6} - 3 y^{4} + 3 y^{2} - y = 0

y = 0, y = 1, y \approx 1.28879 \dots, y \approx 0.38939 \dots

Solution steps

y^{6} - 3 y^{4} + 3 y^{2} - y = 0

Factor

y^{6} - 3 y^{4} + 3 y^{2} - y : y (y - 1) (y^{4} + y^{3} - 2 y^{2} - 2 y + 1)

y (y - 1) (y^{4} + y^{3} - 2 y^{2} - 2 y + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y = 0 or y - 1 = 0 or y^{4} + y^{3} - 2 y^{2} - 2 y + 1 = 0

Solve

y - 1 = 0 : y = 1

Solve

y^{4} + y^{3} - 2 y^{2} - 2 y + 1 = 0 : y \approx 1.28879 \dots, y \approx 0.38939 \dots

The solutions are

y = 0, y = 1, y \approx 1.28879 \dots, y \approx 0.38939 \dots

2 x^{3} - x^{2} - 22 x - 24 = 0

2 x^{3} + 6 x^{2} + 5 x + 2 = 0

4 x^{4} + 12 x^{3} + 5 x^{2} = 0

x^{4} - 6 x^{2} + 10 = 0

- 6 x^{3} - 48 x^{2} - 66 x + 120

What are the solutions to the equation y^6-3y^4+3y^2-y=0 ?
The solutions to the equation y^6-3y^4+3y^2-y=0 are y=0,y=1,y\approx 1.28879…,y\approx 0.38939…
Find the zeros of y^6-3y^4+3y^2-y=0
The zeros of y^6-3y^4+3y^2-y=0 are y=0,y=1,y\approx 1.28879…,y\approx 0.38939…