Answer:
[tex]x=\pm i\text{ or }x=\pm2i[/tex]
Step-by-step explanation:
So we have the equation:
[tex]x^4+5x^2+4=0[/tex]
Let's let u be equal to x². So:
[tex]u^2+5u+4=0[/tex]
Factor:
[tex](u+1)(u+4)=0[/tex]
Zero Product Property:
[tex]u+1=0\text{ or } u+4=0[/tex]
Subtract:
[tex]u=-1\text{ or }u=-4[/tex]
Replace:
[tex]x^2=-1\text{ or }x^2=-4[/tex]
Take square root:
[tex]x=\pm\sqrt{-1}\text{ or }x=\pm\sqrt{-4[/tex]
Simplify:
[tex]x=\pm i\text{ or }x=\pm2i[/tex]
