REMIS: The Collins-Johnson Problem

The formula gives necessary and sufficient conditions on the complex conjugate roots $a \pm bi$ so that there exists a cubic polynomial with a single real $r$ root in $(0,1)$ yet more than one variation is obtained.

a1 := -(1-3*r)*(a**2+b**2)+2*a*r;
a2 := -(2-3*r)*(a**2+b**2)+4*a*r-2*a-r;
coj := ex(r,0<r<1 and a>=1/2 and b>0 and a1<0 and a2>0);

Variant from Loos & Weispfenning

lwcoj := ex(r,0<r<1 and a1<0 and a2>0);

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