What are the solutions to the equation x^3-6x+9=0 ?

The solutions to the equation x^3-6x+9=0 are x=-3,x= 3/2+i(sqrt(3))/2 ,x= 3/2-i(sqrt(3))/2

Find the zeros of x^3-6x+9=0

The zeros of x^3-6x+9=0 are x=-3,x= 3/2+i(sqrt(3))/2 ,x= 3/2-i(sqrt(3))/2

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x^{3} - 6 x + 9 = 0

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

Solution steps

x^{3} - 6 x + 9 = 0

Factor

x^{3} - 6 x + 9 : (x + 3) (x^{2} - 3 x + 3)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 3 = 0 : x = - 3

Solve

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

The solutions are

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

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

12 x^{3} - 5 x + 132 = 0

2 x^{3} - 2 x^{2} - 4 x + 1 = 0

5 x^{9} - x^{2} + 2 x - 3 = 7

x^{3} = 6 x

What are the solutions to the equation x^3-6x+9=0 ?
The solutions to the equation x^3-6x+9=0 are x=-3,x= 3/2+i(sqrt(3))/2 ,x= 3/2-i(sqrt(3))/2
Find the zeros of x^3-6x+9=0
The zeros of x^3-6x+9=0 are x=-3,x= 3/2+i(sqrt(3))/2 ,x= 3/2-i(sqrt(3))/2