Is There More Than One Solution for Cube Root Equations?

[Coco12]

Lets say I was trying to figure out the restrictions of a radical equation and the function inside the radical was a cubic function. I know you have to make the equation inside greater than or equal to 0.
In the case of a quadratic equation, you have to square root it once you bring everything to one side of the equality, giving you a positive and negative answer, is this the same for cube rooting it when figuring out the restrictions? You will have a positive and negative cube root?

 

[jedishrfu]

For a cubic equation there should be three roots once its factored.

Wikipedia has an article on cubic equations that may help:

http://en.wikipedia.org/wiki/Cubic_equation

 

[HallsofIvy]

Lets say I was trying to figure out the restrictions of a radical equation and the function inside the radical was a cubic function. I know you have to make the equation inside greater than or equal to 0.
In the case of a quadratic equation, you have to square root it once you bring everything to one side of the equality, giving you a positive and negative answer, is this the same for cube rooting it when figuring out the restrictions? You will have a positive and negative cube root?

No. (-x)^3= -x^3 so there are not "positive and negative cube roots" of the same number. There will be one real cube root of a real number (other than 0) and two complex conjugate (non-real) roots.

 

[Coco12]

No. (-x)^3= -x^3 so there are not "positive and negative cube roots" of the same number. There will be one real cube root of a real number (other than 0) and two complex conjugate (non-real) roots.

Ok thank you

 

[SteamKing]

If you want to take the nth root of a number, there will be n different roots.

See this article:

http://en.wikipedia.org/wiki/Root_of_unity