# Finding the zeros of a function (algebriacally)

• July 28th 2010, 03:45 PM
danielh9103
Finding the zeros of a function (algebriacally)
f(x) = (-x^2)(e^-x) + 2xe^-x

finding the zeros of this darn function, help please :)
• July 28th 2010, 03:51 PM
Quote:

Originally Posted by danielh9103
f(x) = (-x^2)(e^-x) + 2xe^-x

finding the zeros of this darn function, help please :)

That's the purpose of factoring, writing an expression as a product.

Fact: Zero multiplied by anything is zero because any amount of zeros is zero.

So, can we factor that ?

Yes, there is a common factor $x$ and another $e^{-x}$

$-x^2e^{-x}+2xe^{-x}=xe^{-x}(2-x)=(x)\left(e^{-x}\right)(2-x)$

Now you can see which values of x causes that to be zero.