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

The solutions to the equation 3x^3-2x+1=0 are x=-1,x= 1/2+i(sqrt(3))/6 ,x= 1/2-i(sqrt(3))/6

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

The zeros of 3x^3-2x+1=0 are x=-1,x= 1/2+i(sqrt(3))/6 ,x= 1/2-i(sqrt(3))/6

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

x = - 1, x = \frac{1}{2} + i \frac{3}{6}, x = \frac{1}{2} - i \frac{3}{6}

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 1 = 0 : x = - 1

Solve

3 x^{2} - 3 x + 1 = 0 : x = \frac{1}{2} + i \frac{3}{6}, x = \frac{1}{2} - i \frac{3}{6}

The solutions are

x = - 1, x = \frac{1}{2} + i \frac{3}{6}, x = \frac{1}{2} - i \frac{3}{6}

x^{3} + 0 x^{2} + 0 x + 1 = 0

x^{3} - 15 x = 2 x^{2}

16 x^{3} - 32 x^{2} - x + 2 = 0

a^{3} + (6 - a)^{2} - 36 = 0

- x^{3} + 6 x = 0

What are the solutions to the equation 3x^3-2x+1=0 ?
The solutions to the equation 3x^3-2x+1=0 are x=-1,x= 1/2+i(sqrt(3))/6 ,x= 1/2-i(sqrt(3))/6
Find the zeros of 3x^3-2x+1=0
The zeros of 3x^3-2x+1=0 are x=-1,x= 1/2+i(sqrt(3))/6 ,x= 1/2-i(sqrt(3))/6