Question

f(x) xe^x + e^x, find the zeros

Answer 1

f(x) = xe^x + e^x
Set f(x) = 0 [To calculate the zeroes]

xe^x + e^x = 0
e^x(x+1) = 0

So, either e^x = 0, or (x+1) = 0

Hence, e^x = 0 [when x = \(\infty\)]
(x+1) = 0, [when x = -1]

Zeroes: \(-1, \infty\) [I am not quite sure if infinity is a zero, but hope it makes sense now]