Question

Find all the zeros of the equation. Need help finding the zeros.

-3 x^{4} } +27 x^{2} +1200=0

Answer 1

`x =5\\x =-5\\x=4i\\x=-4i`

Explanation:

We have the equation
`-3x^4 +27 x^(2) +1200=0`

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

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-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

`(x+5)(x-5)(-3x^2 - 48)=0`

`(-3x^2 - 48)` this polynomial has no real roots

`-3x^2 -48 = 0\\\\x^2 + 16 = 0\\\\x = \±\ 4i`

Then we have left:

`(x+5)(x-5)(x-4i)(x+4i)= 0`

And the zeros of the polynomial are:

`x =5\\x =-5\\x=4i\\x=-4i`