Find all the zeroes of the equation. -3x^4 + 27x^2 + 1200 = 0i just want more of an explanation on how to get it .

replace x^2 with m and try to solve

-3 m^2 +27 m +1200 =0

factor out -3

-3(m^2 -9m-400)=0

-3 (m-25) (m+16) =0

using the zero product property

m-25 =0 m+16=0

m=25  m=-16

then substitute m=x^2 back in

x^2 = 25   x^2 = -16

x take the square root of each side

x = +- sqrt (25)   if you know complex number  x = +- sqrt (-16)

x = +-5      x = +- 4i

 +5, -5 , +4i, -4i

.there can be infinite values of m and n that can satisfy the above equation. for each value of m of m or n. there maybe infinite sets of solution for the above

step-by-step explanation:

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