Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$e^{- x} x^{2} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 0$$
Numerical solution$$x_{1} = 99.6706130283057$$
$$x_{2} = 91.720934730719$$
$$x_{3} = 121.570827102163$$
$$x_{4} = 101.659470122749$$
$$x_{5} = 115.593756384128$$
$$x_{6} = 81.8006238116621$$
$$x_{7} = 40.8356618339334$$
$$x_{8} = 50.3607330233137$$
$$x_{9} = 0$$
$$x_{10} = 46.5128714785856$$
$$x_{11} = 35.379255492682$$
$$x_{12} = 64.0255739002577$$
$$x_{13} = 58.1423474863896$$
$$x_{14} = 38.9827879874711$$
$$x_{15} = 77.8395419968606$$
$$x_{16} = 85.7660696193442$$
$$x_{17} = 75.8609058011359$$
$$x_{18} = 42.7114678029016$$
$$x_{19} = 40.5820728530031$$
$$x_{20} = 56.1888924840258$$
$$x_{21} = 103.648824952827$$
$$x_{22} = 83.7828486140689$$
$$x_{23} = 71.9081118282112$$
$$x_{24} = 62.0611807434853$$
$$x_{25} = 73.8837117221529$$
$$x_{26} = 44.6050925906729$$
$$x_{27} = 93.707404744577$$
$$x_{28} = 117.585818346237$$
$$x_{29} = 52.2971932633301$$
$$x_{30} = 67.9624187188197$$
$$x_{31} = 111.610608082484$$
$$x_{32} = 119.578180845004$$
$$x_{33} = 109.619562634492$$
$$x_{34} = 69.9342805013838$$
$$x_{35} = 105.638644821409$$
$$x_{36} = 87.7502050583631$$
$$x_{37} = 37.1602455397125$$
$$x_{38} = 89.7351819043081$$
$$x_{39} = 107.628899840344$$
$$x_{40} = 113.602013088993$$
$$x_{41} = 97.6822895145426$$
$$x_{42} = 54.2402420845623$$
$$x_{43} = 65.9927593677372$$
$$x_{44} = 79.8194870788507$$
$$x_{45} = 60.0999560358985$$
$$x_{46} = 48.4320998819442$$
$$x_{47} = 95.6945389638031$$