Question

Find all the zeroes of the equation. -3x4+27x2+1200=0 I need to learn how to do it! Just not the answer please

Answer 1

The answer are the following: 
 x1 = 5 
 x2 = -5 
x3 = -4i
 x4 = 4i

Step 1: 
We have the equation
 (-1/3) * (- 3x ^ 4 + 27x ^ 2 + 1200) = (- 1/3) * (0)
 x ^ 4-9x ^ 2-400 = 0

Step 2: Write it in polynomial equation
(x-5) * (x + 5) * (x ^ 2 + 16) = 0
(x-5) * (x + 5) * (x+4)(x-4) = 0

From the factored form, we can get the roots which are 
5, -5, 4, -4

Answer 2

The first thing you should do for this case is to rewrite the expression.
 To do this, divide both sides of the equation between -3.
 We have then:
 (-1/3) * (- 3x ^ 4 + 27x ^ 2 + 1200) = (- 1/3) * (0)
 x ^ 4-9x ^ 2-400 = 0
 Then, we rewrite the polynomial:
 (x-5) * (x + 5) * (x ^ 2 + 16) = 0
 From here, we obtain the four roots:
 Root 1:
 x-5 = 0
 x = 5
 Root 2:
 x + 5 = 0
 x = -5
 Root 3 and root 4:
 x ^ 2 + 16 = 0
 x3 = -4i
 x4 = 4i

 Answer:
 all the zeroes of the equation are: 
 x1 = 5 
 x2 = -5
 x3 = -4i
 x4 = 4i