% Cancelation in quadratic formula
% 
% ax^2+bx+c=0
% 
% x=(-b\pm \sqrt{b^2-4ac})/2a
%
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% pick roots and coefficient a 
format long 
x1=1
x2=-0.000000000001
a=1
% a(x-x1)(x-x2) = ax^2-a(x1+x2)x+x1*x2, so
b=-a*(x1+x2)
c=x1*x2
% we can get our roots back from the qudratic formula: 
r1=(-b+sqrt(b^2-4*a*c))/(2*a)
r2=(-b-sqrt(b^2-4*a*c))/(2*a)
% works fine! at least for this choice of coefficients
%
%
% try to do the same for X1=1 and X2=-100000000000