Question

PLEASE HELP ME!

Find all the zeros of the equation
-3x^4+27x^2+1200=0 : Please show the steps used to find the answer thanks a million! :D

Answer 1

Real roots:

x = {-5, 5}

Imaginary roots:

x = {-4i, 4i}

Explanation:

We can solve this via factoring:

`-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`

And so by solving for x we have:

Case 1:

`x-5=0\\\\x=5\\`

Case 2:

`x+5=0\\\\x=-5\\`

Case 3:

`x^2+16=0\\\\x^2=-16\\\\x=√(-16) \\\\x=\pm4i\\`

And so you have two real solutions and two imaginary solutions:

Real:
`x=\pm 5`

Imaginary:
`x=\pm 4i`