What are the solutions to the equation 12x^3+12x^2+12x=0 ?

The solutions to the equation 12x^3+12x^2+12x=0 are x=0,x=-1/2+i(sqrt(3))/2 ,x=-1/2-i(sqrt(3))/2

Find the zeros of 12x^3+12x^2+12x=0

The zeros of 12x^3+12x^2+12x=0 are x=0,x=-1/2+i(sqrt(3))/2 ,x=-1/2-i(sqrt(3))/2

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

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

Solution steps

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

Factor

12 x^{3} + 12 x^{2} + 12 x : 12 x (x^{2} + x + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

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

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

0 = x^{3} - 2 x

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

x^{3} - 7 x^{2} + 9 x + 5 = 0

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

What are the solutions to the equation 12x^3+12x^2+12x=0 ?
The solutions to the equation 12x^3+12x^2+12x=0 are x=0,x=-1/2+i(sqrt(3))/2 ,x=-1/2-i(sqrt(3))/2
Find the zeros of 12x^3+12x^2+12x=0
The zeros of 12x^3+12x^2+12x=0 are x=0,x=-1/2+i(sqrt(3))/2 ,x=-1/2-i(sqrt(3))/2