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

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

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

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

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

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

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

The solutions are

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

x^{4} - 12 x^{2} + 4 = 0

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

a^{3} = - 64

16 x^{4} - 1321 x^{2} + 2025 = 0

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

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