Question

Find all the zeros of the equation.

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

Answer 1

The answer is 5,-5,4i,-4i.

Explanation:

When the equation is divided by -3 it becomes:

`x^4-9*x^2-400=0`

If we factorize the equation, the equation will become as:

`(x+5)*(x-5)*(x^2+16)=0`

That means the equation has 2 real zeros.

`x=5\\x=-5`

Also it has 2 complex zeros also. Those are:

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

Answer 2

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

factor out -3

-3(x^4 -9x^2 -400)=0

divide by -3

x^4 -9x^2 -400=0

(x^2-25) (x^+16) = 0

x^2-25=0 x^2+16=0

(x-5)(x+5)=0 x^2=-16

x=5 x=-5 x = 4i x=-4i

Answer: x=5 x=-5 x = 4i x=-4i