# #y=x^2e^(-x)# has a maximum turning point at #A(2,4/e^2)#. The equation #x^2e^(-x)-2=0# has 3 real, distinct roots. What are the possible values of #k#?

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The answers say #0<k<2# , but I have no idea how to get to this.

Thanks!

The answers say

Thanks!

##### 1 Answer

Nov 27, 2017

See below.

#### Explanation:

The equation

https://en.wikipedia.org/wiki/Lambert_W_function

We have

Now using the property

we have

with the **only** real solution

NOTE

Attached the representation of how to obtain a graphical solution as the intersection of