# How many roots does the equation -2x^3 = 0 have?

Apr 17, 2017

$x = 0$

#### Explanation:

This equation only has one root. We are multiplying $- 2$ by something to give $0$. The only number which could produce this result is $0$.

Thus $x = 0$.

Apr 17, 2017

One with multiplicity 3

#### Explanation:

The equation $- 2 {x}^{3} = 0$ has only one zero, but in fact, they are three roots concentrated in only one.
This is set for deeper reasons (fundamental theorem of Algebra), but an intuitive explanation is that if we change of a little quantity depending on $x$, say $\epsilon x$, we will have three roots:

$- 2 {x}^{3} + \epsilon x = 0 R i g h t a r r o w x \left(- 2 {x}^{2} + \epsilon\right) = 0 R i g h t a r r o w x = 0 , \pm \sqrt{\epsilon}$

This is why we say that $x = 0$ is a root with multiplicity $3$