Answer:
[tex]x =5\\x =-5\\x=4i\\x=-4i[/tex]
Step-by-step explanation:
We have the equation [tex]-3x^4 +27 x^{2} +1200=0[/tex]
Since it is a polynomial of degree 4, to solve it we must use the ruffini method, as shown below.
We start by testing with x = 5 that it is a multiple of 1200.
-3 0 27 0 1200
5 -15 -75 -240 -1200
--------------------------------------------------
-3 -15 -48 -240 0
x = 5 is a root of the polynomial
Now we try with x = -5
-3 -15 -48 -240
-5 15 0 240
---------------------------------------------
-3 0 -48 0
x = -5 is a root of the polynomial
Then we have the following polynomial
[tex](x+5)(x-5)(-3x^2 - 48)=0[/tex]
[tex](-3x^2 - 48)[/tex] this polynomial has no real roots
[tex]-3x^2 -48 = 0\\\\x^2 + 16 = 0\\\\x = \±\ 4i[/tex]
Then we have left:
[tex](x+5)(x-5)(x-4i)(x+4i)= 0[/tex]
And the zeros of the polynomial are:
[tex]x =5\\x =-5\\x=4i\\x=-4i[/tex]
