Answer :
[tex]x^4+x^2-6=0 \\
(x^2)^2+x^2-6=0 \\ \\
a=1 \\ b=1 \\ c=-6 \\ b^2-4ac=1^2-4 \times 1 \times (-6)=1+24=25 \\ \\
x^2=\frac{-b \pm \sqrt{b^2-4ac}}{2a}=\frac{-1 \pm \sqrt{25}}{2 \times 1}=\frac{-1 \pm 5}{2} \\
x^2=\frac{-1-5}{2} \ \lor \ x^2=\frac{-1+5}{2} \\
x^2=\frac{-6}{2} \ \lor \ x^2=\frac{4}{2} \\
x^2=-3 \ \lor \ x^2=2 \\
x=\pm \sqrt{-3} \ \lor \ x=\pm \sqrt{2} \\
\boxed{x=-i\sqrt{3} \hbox{ or } x=i\sqrt{3} \hbox{ or } x=-\sqrt{2} \hbox{ or } x=\sqrt{2}}[/tex]
[tex]x^4+x^2-6=0\\
x^4+3x^2-2x^2-6=0\\
x^2(x^2+3)-2(x^2+3)=0\\
(x^2-2)(x^2+3)=0\\
x^2-2=0 \vee x^2+3=0\\
x^2=2 \vee x^2=-3\\
x=-\sqrt2 \vee x=\sqrt2 \vee x=-i\sqrt3 \vee x=i\sqrt3[/tex]
