1. ## Intermediate problem

Hi, I'm new to this forum, so apologies if I'm posting this question on the wrong board - the other posts on the pre-algebra board seemed more basic than this. The problem is: solve for x in: x*exp(-x^2) = 0. I know x must be zero just by looking at the function, but I don't know how to show this algebraically. Thanks in advance.

2. Originally Posted by bsk
Hi, I'm new to this forum, so apologies if I'm posting this question on the wrong board - the other posts on the pre-algebra board seemed more basic than this. The problem is: solve for x in: x*exp(-x^2) = 0. I know x must be zero just by looking at the function, but I don't know how to show this algebraically. Thanks in advance.
Okay, do you know that when you have a product(s) equal to 0, you set each piece to equal zero. What I mean is:

If $ab=0$ then $a = 0$ or $b = 0$

Similarly:
$xe^{-x^2} = 0$

$x = 0$ or $e^{-x^2} = 0$

So you know that one solution is $x = 0$, but there could be another one, when you solve the other equation.

$e^{-x^2} = 0 \implies \ln0 = x^2$

You need to realize that the domain of the natural logarithm function is strictly greater than 0. Since the left side does not exist, there is no solution to this equation. (You might have noticed it before because exp(anything) can't equal 0.

This means your only solution is $x = 0$.

Hope I helped you

3. Many thanks - I knew I was going to kick myself

4. Originally Posted by bsk
Many thanks - I knew I was going to kick myself
You are very welcome!

Just remember, if you see x in a product expression on one side of the equation and 0 on the other, don't immediately assume x=0 is the only solution. It will be one, but it is very likely that there will be another.