Following are the calculation to find the zeros of the equation:
Given:
[tex]\bold{-3x^4 + 27x^2 + 1200 = 0}[/tex]
To find:
zeros=?
Solution:
[tex]\bold{-3x^4 + 27x^2 + 1200 = 0}[/tex]
taking the '-3' from the above equation:
[tex]\bold{-3(x^4 - 9x^2 + 400) = 0}\\\\\bold{ x^4 - 9x^2 + 400 = 0}\\\\[/tex]
Using the AC method for Factor the above equation:
[tex](x^2 - 25) (x^2 + 16) = 0\\\\\therefore\\\\\to (a^2-b^2)=(a+b)(a-b)\\\\(x^2 - 5^2) (x^2 + 16) = 0\\\\(x - 5) (x+5) (x^2 + 16) = 0\\\\\because\\\\x-5=0 \ \ \ \ \ \ \ x+5=0 \ \ \ \ \ \ \ x^2+16=0\\\\x=5 \ \ \ \ \ \ \ x= -5 \ \ \ \ \ \ \ x^2= -16\\\\x=5 \ \ \ \ \ \ \ x= -5 \ \ \ \ \ \ \ x^2= -4^2\\\\x=5 \ \ \ \ \ \ \ x= -5 \ \ \ \ \ \ \ x= \pm 4i\\\\\\x= \pm 5 \ \ and \pm 4i[/tex]
Therefore, the final answer is "[tex]x= \pm 5 \ \ and \pm 4i[/tex]".
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