[tex]x^4+3x^2+2=0\\\\\text{substitute}\ x^2=t\\\\t^2+3t+2=0\\\\t^2+t+2t+2=0\\\\t(t+1)+2(t+1)=0\\\\(t+1)(t+2)=0\iff t+1=0\ \vee\ t+2=0\\\\t=-1\ \vee\ t=-2\\\\t=x^2\ \text{therefore}\\\\x^2=-1\ \vee\ x^2=-2\\\\x=\pm\sqrt{-1}\ \vee\ x=\pm\sqrt{-2}\\\\x=\pm i\ \vee\ x=\pm i\sqrt2[/tex]
