f(x) = 3*e-6x(x4 -x5) = 0
In order for this to be true, either 3*e-6x = 0 or (x4 - x5) = 0
(x4 - x5) = 0 when x = 1
When x = 0, however, the quantity 3x4e-6x - 3x5e-6x is clearly 0 (by virtue of the x4 and x5 terms) so the origin (0, 0) is one of the two roots.
Note that the quantity 3*e-6x never truly reaches zero. It approaches 0 asymptotically at -∞, but fails to actually achieve 0.
The smaller root is x = 0
The bigger root is x = 1