Answer:
Real roots:
x = {-5, 5}
Imaginary roots:
x = {-4i, 4i}
Step-by-step explanation:
We can solve this via factoring:
[tex]-3x^4+27x^2+1200=0\\\\-3(x^4-9x^2-400)=0\\\\-3(x^4+16x^2-25x^2-400)=0\\\\-3(x^2(x^2+16)-25(x^2+16))=0\\\\-3(x^2-25)(x^2+16)=0\\\\-3(x^2-(5)^2)(x^2+16)=0)\\\\-3(x-5)(x+5)(x^2+16)=0[/tex]
And so by solving for x we have:
Case 1:
[tex]x-5=0\\\\x=5\\[/tex]
Case 2:
[tex]x+5=0\\\\x=-5\\[/tex]
Case 3:
[tex]x^2+16=0\\\\x^2=-16\\\\x=\sqrt{-16} \\\\x=\pm4i\\[/tex]
And so you have two real solutions and two imaginary solutions:
Real: [tex]x=\pm 5[/tex]
Imaginary: [tex]x=\pm 4i[/tex]
