y=x^2e^x-2xe^x+2e^x?

Answer 1

What is the question??

Answer 2

Using bequalming's idea:

y = e^x (x^2 - 2x +2)

y(-1)= e^-1 (1 +2 +2) = 5/e
y(0) = e^0 (2) = 2
y(1) = e (1-2+2) = e
y(2) = e^2 (4-4+2) = 2 e^2

e^x is strictly positive for all values of x.
(x^2 -2x +2) is strictly positive for all values of x (minimum at x=1)

Therefore the product is always strictly positive (y has no real roots)

Answer 3

factor out the e^x