Solve X² = 0: Step-by-Step Guide for Beginners

  • Thread starter lakitu
  • Start date
In summary, the conversation discusses solving the equation x² = 0 and the conclusion is that the only solution is x = 0. There is a brief mention of using fractions and factoring, but ultimately it is agreed upon that there is no such thing as positive or negative zero. The conversation also touches on the concept of nilpotent operators in linear spaces.
  • #1
lakitu
27
0
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
 
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  • #2
You could take the square root of both sides. -0 is the same as 0.
 
  • #3
Same way you would solve an equation of the form x2= a for any non-negative a: take the square root of both sides: [itex]x= \pm\sqrt{a}[/itex].

[itex]x= \pm 0[/itex] but since -0= 0, there is only the solution x= 0.
 
  • #4
It's just zero (there's no such thing as positive zero or negative zero).
 
  • #5
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) :redface:
 
  • #6
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
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
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
there is no such thing as -0 or +0
Sure there is. They're both equal to 0.
 
  • #10
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
Very deep precalculus maths that, dexter.
 

1. What is the general approach to solving x² = 0?

The general approach to solving x² = 0 is to use the fact that any number multiplied by 0 is equal to 0. This means that in order for x² to be equal to 0, x must be equal to 0. Therefore, the solution to x² = 0 is simply x = 0.

2. What is the first step to solving x² = 0?

The first step to solving x² = 0 is to isolate the squared term on one side of the equation. In this case, we can subtract x² from both sides to get 0 = -x². This leaves us with a simplified equation that is easier to work with.

3. Can x be any number when solving x² = 0?

No, x cannot be any number when solving x² = 0. As mentioned earlier, the only solution to this equation is x = 0. This is because any number squared will always result in a positive number, except for 0. Therefore, in order for x² to be equal to 0, x must be 0.

4. What is the difference between solving x² = 0 and solving x² = 1?

The difference between solving x² = 0 and solving x² = 1 is that x = 0 is the only solution to the equation x² = 0, while x = 1 and x = -1 are both solutions to the equation x² = 1. This is because when x = 1 or x = -1, the squared term will equal 1, satisfying the equation.

5. Can the steps for solving x² = 0 be applied to other equations?

Yes, the steps for solving x² = 0 can be applied to other equations that have a squared term equal to 0. The general approach is to isolate the squared term and then solve for the variable by taking the square root of both sides. However, it is important to note that the solutions may not always be as simple as x = 0, and additional steps may be required.

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