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

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

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

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

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

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

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

The solutions are

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

t^{3} - 2 t = 4

2 x^{3} - 5 = 0

5 x^{3} - 125 x = 0

x^{4} + 5 x^{3} - 7 x^{2} - 8 x - 12 = 0

2 x^{3} + x^{2} - 7 x - 6 = 0

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