Answer:
0 and 2
Step-by-step explanation:
[tex]f(x) = -x^2e^{-x}+2xe^{-x}[/tex]
To find zeros set f(x)=0 and solve for x
[tex]0 = -x^2e^{-x}+2xe^{-x}[/tex]
[tex]0 = -e^{-x}(x^2-2x)[/tex]
now factor out x
[tex]0 = -xe^{-x}(x-2)[/tex]
set each factor =0 and solve for x
[tex]x=0[/tex]
[tex]-e^{-x}=0[/tex] no solution for x
[tex]x-2=0, x=2[/tex]
zeros of f are 0 and 2
