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

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

Find the zeros of roots m^4+m^3+m^2=0

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

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roots

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

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

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

The solutions are

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

x^{3} + 3 x^{2} - 24 x - 72 = 0

5 x^{3} + x^{2} - 20 x - 4 = 0

10 x^{4} - 20 x^{3} - 30 x^{2} = 0

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

x^{3} - 5 x^{2} - 9 x + 45 = 0

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