\\$From $ x^2+2x+3=0,\\\prod \alpha =H \times K=H \times \overline{H}=K \times \overline{K}=3\\$But $H \times \overline{H}=|H|^2=K \times \overline{K}=|K|^2\\\therefore |H|=|K|=\sqrt{3}\\$From $ x^2+2px+q=0,\\\prod \alpha =A \times B=A \times \overline{A}=B \times \overline{B}=q\\$But $A \times...