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

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

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

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

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

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

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

3 x - 2 = 0 : x = \frac{2}{3}

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

t (t^{2} - 5 t + 14) = 0

2170 = \frac{4}{3} π r^{3}

z^{4} = 2 + 2 i

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

5 x^{3} + 4 x = 0

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