Print the quantifier-free formula in logic formula form

$\mathrm{with}\left(\mathrm{RegularChains}\right)\:$

$\mathrm{with}\left(\mathrm{ParametricSystemTools}\right)\:$

$\mathrm{with}\left(\mathrm{SemiAlgebraicSetTools}\right)\:$

$R≔\mathrm{PolynomialRing}\left(\left[x\,b\,a\,c\right]\right)$

$R≔\mathrm{polynomial\_ring}$

$F≔\left[a{x}^2\+bx\+c\right]$

$F≔\left[a{x}^2+bx+c\right]$

$N≔\left[\right]$

$N≔\left[\right]$

$P≔\left[x\right]$

$P≔\left[x\right]$

$H≔\left[a\right]$

$H≔\left[a\right]$

$\mathrm{rrc}≔\mathrm{RealRootClassification}\left(F\,\left[\right]\,\left[x\right]\,\left[a\right]\,3\,2\,R\right)$

$\mathrm{rrc}≔\left[\left[\mathrm{regular\_semi\_algebraic\_set}\right]\,\mathrm{border\_polynomial}\right]$

$\mathrm{rsas}≔{{\mathrm{rrc}}_1}_1$

$\mathrm{rsas}≔\mathrm{regular\_semi\_algebraic\_set}$

$\mathrm{pbx}≔\mathrm{RepresentingBox}\left(\mathrm{rsas}\,R\right)$

$\mathrm{pbx}≔\mathrm{parametric\_box}$

$\mathrm{qff}≔\mathrm{RepresentingQuantifierFreeFormula}\left(\mathrm{pbx}\right)$

$\mathrm{qff}≔\mathrm{quantifier\_free\_formula}$

$\mathrm{DisplayQuantifierFreeFormula}\left(\mathrm{qff}\right)\:$

$c<0\mathbf{and}a<0\mathbf{and}b>0\mathbf{and}4ac-b^2<0$

$\mathbf{or}c>0\mathbf{and}a>0\mathbf{and}b<0\mathbf{and}4ac-b^2<0$