What are the solutions to the equation 3x^3-x^2+6x-2=0 ?

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

Find the zeros of 3x^3-x^2+6x-2=0

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

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

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

Solution steps

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

Factor

3 x^{3} - x^{2} + 6 x - 2 : (3 x - 1) (x^{2} + 2)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

3 x - 1 = 0 : x = \frac{1}{3}

Solve

x^{2} + 2 = 0 : x = 2 i, x = - 2 i

The solutions are

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

\frac{1}{64} = X^{3}

x, 2 x^{3} + 4 x^{2} - 9 = 0

- x^{3} + 9 x^{2} - 26 x + 24 = 0

x^{5} + 26 x^{3} - 36 = 0

z^{3} + z - 10 = 0

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