0=x^3+2x Need the answer and the how?

Question

Need to figure out what the answer is to set this to zero in order to include it in a 4 page term paper. Help please? I'm not good at this format of a problem. Thanks!

Answer 1

First step: factor.

x^3 + 2x = 0

x(x^2 + 2) = 0
Therefore,
x = 0 and x^2 + 2 = 0

or

x = 0 and x^2 = -2

The former is a solution, the latter doesn't have any (real) solutions. If you want the complex solution of x^2 + 2 = 0, the answer is x = +/- sqrt(2)*i

Answer 2

Don't know much about math, but my guess would be that the solution for the variable is zero. I think that because I can't see how adding two positive or two negatives will ever give you zero. Try it.

Let X = 1
1^3 +2(1) = 1 + 2 = 3

Let X = -1
-1^3 + 2(-1) = -1 + (-2) = -3

Let X = 0
0^3 + 2(0) = 0 + 0 = 0

Answer 3

Factor out the common x:

0 = X(X^2 + 2)

Set each term equal to 0;

x = 0

x^2 + 2 = 0
x^2 = -2
x = sqrt -2
There is no answer for this value of x as the sqrt of -2 cannot be a negative number.

Answer 4

take an x out of the equation, so you get x(x^2 + 2) = 0

then from there you know that f(x) = 0 if x=0 (from the first x, outside the brackets)

then you are left with x^2 + 2 = 0, if you subtract 2 from each side, and then square root each side, you are left with the square root of a negative number which you cannot do. (unless non-real numbers, but cant help you there, don't know much about them)

So the answer is f(x) = 0 if x = 0. It makes sense if you think about it, as it is x^3 + 2x you can never get 0, if you plug in negative number you get a negative plus a negative. If you plug in positive numbers you get positive plus positive.

I think that is what you are asking, hope it helps.

Answer 5

X is either 0 or Squareroot(2) * i wherby i = imaginary number or squareroot(-1)