What are the solutions to the equation 3x^3-2x^2+12x-8=0 ?

The solutions to the equation 3x^3-2x^2+12x-8=0 are x= 2/3 ,x=2i,x=-2i

Find the zeros of 3x^3-2x^2+12x-8=0

The zeros of 3x^3-2x^2+12x-8=0 are x= 2/3 ,x=2i,x=-2i

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

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

Solution steps

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

Factor

3 x^{3} - 2 x^{2} + 12 x - 8 : (3 x - 2) (x^{2} + 4)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Solve

x^{2} + 4 = 0 : x = 2 i, x = - 2 i

The solutions are

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

x^{4} - 4 x^{3} + 2 x^{2} - 5 x + 7 = 0

4 x^{4} - 4 x^{2} - 1 = 0

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

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

(x^{3} - 27) = 0

What are the solutions to the equation 3x^3-2x^2+12x-8=0 ?
The solutions to the equation 3x^3-2x^2+12x-8=0 are x= 2/3 ,x=2i,x=-2i
Find the zeros of 3x^3-2x^2+12x-8=0
The zeros of 3x^3-2x^2+12x-8=0 are x= 2/3 ,x=2i,x=-2i