what are the solutions of the equation x4+3x2+2=0? use u substitution to solve

ANSWER[tex]x = \: x = \pm \: \sqrt{2} i \: or \: x = \pm \: i[/tex]EXPLANATION[tex] {x}^{4} + 3 {x}^{2} + 2 = 0[/tex][tex]{ ({x}^{2}) }^{2} + 3( {x}^{2}) + 2 = 0[/tex]Let [tex]u = {x}^{2} [/tex]Then the equation becomes:[tex] {u}^{2} + 3u + 2 = 0[/tex][tex] {u}^{2} + 3u + 2 = 0[/tex][tex] {u}^{2} + 2u +u + 2 = 0[/tex]Factor:[tex]{u}(u + 2)+ 1(u + 2) = 0[/tex][tex](u + 1)(u + 2) = 0[/tex][tex]u = - 1[/tex]or[tex]u = - 2[/tex]This implies that[tex] {x}^{2} = - 1 \implies \: x = \pm \: i[/tex]or[tex] {x}^{2} = - 2 \implies \: x = \pm \: \sqrt{2} i[/tex]