What are the solutions to the equation 0=θ^1+θ^2+θ^3 ?

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

Find the zeros of 0=θ^1+θ^2+θ^3

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

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0 = θ^{1} + θ^{2} + θ^{3}

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

Solution steps

0 = θ^{1} + θ^{2} + θ^{3}

Switch sides

θ^{1} + θ^{2} + θ^{3} = 0

Factor

θ^{1} + θ^{2} + θ^{3} : θ (θ^{2} + θ + 1)

θ (θ^{2} + θ + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

θ = 0 or θ^{2} + θ + 1 = 0

Solve

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

The solutions are

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

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

2 x^{3} + x^{2} - 1 = 1

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

x^{2} (x + 1) = 252

(x - 2) (x + 9) (x - 1) = 0

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