Answer:
[tex]\pm i\sqrt{2}\text{ and } \pm i[/tex]
Step-by-step explanation:
[tex]\text{let u = } x^2[/tex] so then [tex]u^2=x^4[/tex].
This gives you the equation: [tex]u^2+3u+2=0[/tex].
Now factor the equation by looking for factors of 2 that add up to 3, which is just 2 and 1. Use these to rewrite the equation: [tex](u+2)(u+1)[/tex]. So now just set each factor equal to 0:
[tex]u+2=0\\u=-2[/tex]
Now substitute x^2 back in as u
[tex]x^2=-2[/tex]
Take the square root of both sides
[tex]x=\pm \sqrt{-2}[/tex]
Separate the radical into sqrt(-1) * sqrt(2)
[tex]x=\pm \sqrt{-1}*\sqrt{2}[/tex]
Rewrite using i
[tex]x=\pm i\sqrt{2}[/tex]
Now set the other factor equal to 0
[tex]u+1=0\\u=-1[/tex]
substitute x^2 back in as u
[tex]x^2=-1[/tex]
Take the square root of both sides
[tex]x=\pm\sqrt{-1}[/tex]
rewrite using i
[tex]x=\pm i[/tex]
