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

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

Find the zeros of 3z^3-2z^2+2z+1=0

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

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3 z^{3} - 2 z^{2} + 2 z + 1 = 0

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

Solution steps

3 z^{3} - 2 z^{2} + 2 z + 1 = 0

Factor

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

(3 z + 1) (z^{2} - z + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

3 z + 1 = 0 or z^{2} - z + 1 = 0

Solve

3 z + 1 = 0 : z = - \frac{1}{3}

Solve

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

The solutions are

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

u^{4} - 5 u^{2} + 6 = 0

8 x^{3} - 12 x^{2} - 24 x = 0

x^{3} + 9 x - 8 = 0

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

x^{4} + x^{3} + 2 x^{2} - x = 4.1151

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