# X² = 0

1. Mar 13, 2006

### lakitu

I was just wondering how to solve the following equation. x² = 0. I am new to algebra and am just unsure as how to solve this.

I have come to the conclusion that the answer is x = 0 or x = -0

Is there any working out needed to be done? This is for homework :)

Kind regards

lakitu

2. Mar 13, 2006

### 0rthodontist

You could take the square root of both sides. -0 is the same as 0.

3. Mar 13, 2006

### HallsofIvy

Staff Emeritus
Same way you would solve an equation of the form x2= a for any non-negative a: take the square root of both sides: $x= \pm\sqrt{a}$.

$x= \pm 0$ but since -0= 0, there is only the solution x= 0.

4. Mar 13, 2006

### BobG

It's just zero (there's no such thing as positive zero or negative zero).

5. Mar 13, 2006

### Lisa!

what's the point in solving such a equation? At first I though I was missing some point.(I guess OP was feeling the same way)

6. Mar 13, 2006

### lakitu

yeah I thought it was odd to being that there is no such thing as -0 or +0 here is the question he gave me.

Solve the equation
x² = 0
x = ? or x = ?

7. Mar 13, 2006

### wScott

Well I've been doing algebra for several chool years and the only way I could think that he would expect you to find x would be to put x = 0. You could also use fractions, but I don't think he expects youto know that yet.

8. Mar 13, 2006

### chroot

Staff Emeritus
Fractions, wScott? There are no fractional roots. There is only one (degenerate) solution of this polynomial, x=0.

You can factor x^2 = 0 as (x + 0)(x + 0) = 0.

- Warren

9. Mar 13, 2006

### Hurkyl

Staff Emeritus
Sure there is. They're both equal to 0.

10. Mar 14, 2006

### dextercioby

What if "x" is an operator on some linear space...? You know, just because d^{2}=0 for the exterior differential, it doesn't mean that d=0...Such operators are called "nilpotent of degree "n" if d^{n}=0 on some linear space...

Daniel.

11. Mar 14, 2006

### arildno

Very deep precalculus maths that, dexter.