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

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

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

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

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

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

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

4 x^{3} + 12 x^{2} + 16 x = 0

x^{4} - 6 x^{3} + 6 x^{2} - 6 x + 5 = 0

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

z, (a) z^{4} = 24 i - 7

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

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