Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\sqrt{x} e^{x} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 0$$
Numerical solution$$x_{1} = -120.968348080616$$
$$x_{2} = -63.0791364380438$$
$$x_{3} = -94.9986434020122$$
$$x_{4} = -100.990069110598$$
$$x_{5} = -98.9927946593729$$
$$x_{6} = -49.1600217512013$$
$$x_{7} = -31.4710200385529$$
$$x_{8} = -53.1309970905921$$
$$x_{9} = -89.0085679306054$$
$$x_{10} = -73.0447315518853$$
$$x_{11} = -61.0877539258535$$
$$x_{12} = -51.1447223743512$$
$$x_{13} = -67.0638346231616$$
$$x_{14} = -96.9956495959489$$
$$x_{15} = -33.4042694137578$$
$$x_{16} = -71.0506578790373$$
$$x_{17} = -69.0570095659301$$
$$x_{18} = -106.982586137274$$
$$x_{19} = -59.0971307960406$$
$$x_{20} = -55.1186108210408$$
$$x_{21} = -112.975997979872$$
$$x_{22} = -91.0050904444827$$
$$x_{23} = -43.2187501477016$$
$$x_{24} = -87.01223309669$$
$$x_{25} = -114.973973493728$$
$$x_{26} = 0$$
$$x_{27} = -57.1073737496955$$
$$x_{28} = -79.0291136628044$$
$$x_{29} = -45.1966038596489$$
$$x_{30} = -85.0161016524756$$
$$x_{31} = -93.0017865135215$$
$$x_{32} = -77.0339935679106$$
$$x_{33} = -39.2740530264455$$
$$x_{34} = -37.3093090541517$$
$$x_{35} = -83.0201911227922$$
$$x_{36} = -102.987464315167$$
$$x_{37} = -116.972026550028$$
$$x_{38} = -118.970152765141$$
$$x_{39} = -108.980298944191$$
$$x_{40} = -41.2442746296924$$
$$x_{41} = -65.0711886544365$$
$$x_{42} = -81.0245211192852$$
$$x_{43} = -47.1771902579016$$
$$x_{44} = -110.978104750617$$
$$x_{45} = -75.0391889040362$$
$$x_{46} = -104.984972392956$$
$$x_{47} = -35.3518165130442$$
$$x_{48} = -29.5597318722168$$