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+clear all
+clc
+close
+
+a=7.5*1e5;
+b=-4*1e4;
+c=43.75;
+p = poly([c, b,a], 'x', 'c');
+alpha=roots(p);
+printf('Minimum distance measured from the cathode at which an electron may start an avalanche having a size of 1E19 is (in m) %f',alpha(2))