%% The optimal LC which belongs to the NS of type [-1,x2,1] is m=5/4.
%%
%% polys
%%
   x^2+(-x2+1)x+(-m x2+m-1)
   x^2+(-x2-1)x+(m x2+m-1)
%%
%% input formula QEPCAD
%% 
   (Ex2)(Ax)[[-1<x2 /\ x2<1]/\[[-1<=x /\ x<x2] ==> x^2+(-x2+1)x+(-m x2+m-1)>=0] /\ [[x2<x /\ x<=1] ==> x^2+(-x2-1)x+(m x2+m-1)>=0]].
%%
%% input formula MMA
%%
   Exists[x2,-1<x2<1\[And]ForAll[x,(-1<=x<x2\[Implies]x^2+(-x2+1)x+(-m x2+m-1)>=0)\[And](x2<x<=1\[Implies]x^2+(-x2-1)x+(m x2+m-1)>=0)]]