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

The solutions to the equation 3x^3-2x^2-2x+3=0 are x=-1,x= 5/6+i(sqrt(11))/6 ,x= 5/6-i(sqrt(11))/6

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

The zeros of 3x^3-2x^2-2x+3=0 are x=-1,x= 5/6+i(sqrt(11))/6 ,x= 5/6-i(sqrt(11))/6

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

x = - 1, x = \frac{5}{6} + i \frac{11}{6}, x = \frac{5}{6} - i \frac{11}{6}

Solution steps

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

Factor

3 x^{3} - 2 x^{2} - 2 x + 3 : (x + 1) (3 x^{2} - 5 x + 3)

(x + 1) (3 x^{2} - 5 x + 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or 3 x^{2} - 5 x + 3 = 0

Solve

x + 1 = 0 : x = - 1

Solve

3 x^{2} - 5 x + 3 = 0 : x = \frac{5}{6} + i \frac{11}{6}, x = \frac{5}{6} - i \frac{11}{6}

The solutions are

x = - 1, x = \frac{5}{6} + i \frac{11}{6}, x = \frac{5}{6} - i \frac{11}{6}

x^{3} + 3 x^{2} - 7 x - 21 = 0

(x^{2} + 7)^{2} = 0

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

- x^{3} + 6 x^{2} - 10 x + 4 = 0

4 x^{3} - 12 x^{2} = 0

What are the solutions to the equation 3x^3-2x^2-2x+3=0 ?
The solutions to the equation 3x^3-2x^2-2x+3=0 are x=-1,x= 5/6+i(sqrt(11))/6 ,x= 5/6-i(sqrt(11))/6
Find the zeros of 3x^3-2x^2-2x+3=0
The zeros of 3x^3-2x^2-2x+3=0 are x=-1,x= 5/6+i(sqrt(11))/6 ,x= 5/6-i(sqrt(11))/6