Answer:
[tex]x=\pm5,\ x=\pm4i[/tex]
Step-by-step explanation:
[tex]-3x^4+27x^2+1200=0[/tex]
Divide each side by [tex]-3[/tex]
[tex]x^4-9x^2-400=0\\x^4-25x^2+16x^2-400=0\\x^2(x^2-25)+16(x^2-25)=0\\(x^2-25)(x^2+16)[/tex]
When [tex]x^2-25=0[/tex]
[tex]x^2=25[/tex]
Take square root of both sides
[tex]x=\pm\sqrt{25}\\x=\pm5[/tex]
[tex] when\ x^2+16=0\\x^2=-16\\x^2=16x^2\ (as\ i^2=-1)[/tex]
take square root of both side
[tex]x=\pm\sqrt{ 16i^2}\\x=\pm4i[/tex]
