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 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

Answer 2

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