Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\left(x - 2\right)^{2} e^{- x} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 2$$
Numerical solution$$x_{1} = 64.0611807434853$$
$$x_{2} = 115.602013088993$$
$$x_{3} = 46.6050925906729$$
$$x_{4} = 62.0999560358985$$
$$x_{5} = 60.1423474863896$$
$$x_{6} = 35.6579430943359$$
$$x_{7} = 42.5820728530031$$
$$x_{8} = 48.5128714785856$$
$$x_{9} = 50.4320998819442$$
$$x_{10} = 95.707404744577$$
$$x_{11} = 99.6822895145426$$
$$x_{12} = 58.1888924840258$$
$$x_{13} = 39.1602455397125$$
$$x_{14} = 101.670613028306$$
$$x_{15} = 52.3607330233137$$
$$x_{16} = 87.7660696193442$$
$$x_{17} = 85.7828486140689$$
$$x_{18} = 81.8194870788507$$
$$x_{19} = 2$$
$$x_{20} = 56.2402420845623$$
$$x_{21} = 37.379255492682$$
$$x_{22} = 93.720934730719$$
$$x_{23} = 119.585818346237$$
$$x_{24} = 67.9927593677372$$
$$x_{25} = 66.0255739002577$$
$$x_{26} = 69.9624187188197$$
$$x_{27} = 71.9342805013838$$
$$x_{28} = 117.593756384128$$
$$x_{29} = 83.8006238116621$$
$$x_{30} = 97.6945389638031$$
$$x_{31} = 109.628899840344$$
$$x_{32} = 79.8395419968606$$
$$x_{33} = 105.648824952827$$
$$x_{34} = 89.7502050583631$$
$$x_{35} = 54.2971932633301$$
$$x_{36} = 107.638644821409$$
$$x_{37} = 103.659470122749$$
$$x_{38} = 40.9827879874711$$
$$x_{39} = 77.8609058011359$$
$$x_{40} = 42.8356618339334$$
$$x_{41} = 44.7114678029016$$
$$x_{42} = 73.9081118282112$$
$$x_{43} = 113.610608082484$$
$$x_{44} = 75.8837117221529$$
$$x_{45} = 91.7351819043081$$
$$x_{46} = 111.619562634492$$
$$x_{47} = 121.578180845004$$