Solve the equation (x^2)(e^x) - 2x(e^x) = 0?

Answer 1

(x^2)(e^x) - 2x(e^x) = 0
e^x x(x - 2) = 0

Therefore:
x = 0
x = 2

e^x can never be 0.

Answer 2

Factorize left hand side of the equation and write it as:

(e^x)*x(x - 2) = 0.

Now e^x can never be zero for any real finite value of x because e > 2. So either x = 0 or x - 2 = 0 ---> x = 2.

Therefore solutions are x = 0 or x = 2.

Answer 3

In factored form the equation is x*(e^x)*(x - 2) = 0. Therefore either x = 0 or x - 2 = 0, because e^x is never 0. Thus, x = 0 or x = 2.

Answer 4

Try x = 2. It works for me. Also x = 0.

Answer 5

if you write it as
x²e^x = 2xe^x and divide by e^x (which you can do assuming it's not 0), you get
x² = 2x
x² - 2x = 0
x(x-2) = 0
x = 0 or x = 2.
in order for e^x to be 0 we'd need x = -∞, which isn't a solution.