Answer:
5, -5 , 4i, -4i
Explanation:
-3x^4+27x^2+1200=0
graph to get a guess at the roots
you can also use the rational root theorem, but that will give you a lot of guesses
using the graph let x =5
put the coefficients on the first line
put your guess on the outside
-3 0 27 0 1200
5
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bring the first number straight down
-3 0 27 0 1200
5
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-3
multiply the first number by the number on the outside (-3*5 =15)
this number goes under the 2nd coefficient
-3 0 27 0 1200
5 -15
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-3
add the column ( 0+-15) = -15 that number goes under the line
-3 0 27 0 1200
5 -15
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-3 -15
multiply the -15 * 5 = -75
-3 0 27 0 1200
5 -15 -75
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-3 -15
add 27+ -75 = -48
-3 0 27 0 1200
5 -15 -75
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-3 -15 -48
multiply - 48 * 5 = -240
-3 0 27 0 1200
5 -15 -75 -240
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-3 -15 -48
add 0+-240
-3 0 27 0 1200
5 -15 -75 -240
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-3 -15 -48 -240
multiply - 240 * 5 = -1200
add
-3 0 27 0 1200
5 -15 -75 -240 -1200
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-3 -15 -48 -240 0
if it is a root the last number is 0
5 is a root
now take the last line without the zero and try again with another guess
-3 -15 -48 -240
-5
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I will skip the step by step
-3 -15 -48 -240
-5 15 0 240
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- 3 0 -48 0
so -5 is also a root
-3x^2 - 48 =0 is left
-3x^2 = 48
x^2 = 48/-3
x^2 = -16
there are imaginary roots left
take the square root
sqrt(x^2) =± sqrt(-16)
x = ± sqrt(-1)sqrt(16)
remember sqrt(-1) = i
x = ± i4
x = ± 4i
Since this was a 4th degree polynomial, this has 4 roots