What are the solutions to the equation factor x^3+1=0 ?

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

Find the zeros of factor x^3+1=0

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

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factor

x^{3} + 1 = 0

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

Solution steps

x^{3} + 1 = 0

Factor

x^{3} + 1 : (x + 1) (x^{2} - x + 1)

(x + 1) (x^{2} - x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x^{2} - x + 1 = 0

Solve

x + 1 = 0 : x = - 1

Solve

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

The solutions are

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

10 x^{3} = (\frac{4}{3}) π a^{3}

x^{4} - 28 x^{3} + 288 x^{2} - 1116 x + 1296 = 0

5 x^{4} + 1 = 0

2 x^{3} - 3 x^{2} - 12 x + 3 = 0

x^{3} - 2 x^{2} + 16

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