What are the zeros of the function -3x^4+27^2+1200=0 using synthetic division? explain.

5, -5 , 4i, -4i

Step-by-step 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

   ---------------------------------------------------

bring the first number straight down

         -3      0    27         0     1200

5

   ---------------------------------------------------

       -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

   ---------------------------------------------------

       -3      

add the column  ( 0+-15) = -15 that number goes under the line

         -3      0      27         0     1200

5                 -15

   ---------------------------------------------------

       -3      -15

multiply the -15 * 5 = -75

         -3      0      27         0     1200

5               -15   -75

   ---------------------------------------------------

       -3      -15

add 27+ -75 = -48

         -3      0      27         0     1200

5               -15   -75

   ---------------------------------------------------

       -3      -15    -48

multiply - 48 * 5 = -240

         -3      0      27         0     1200

5               -15   -75        -240

   ---------------------------------------------------

       -3      -15    -48

add 0+-240

         -3      0      27         0     1200

5               -15   -75        -240

   ---------------------------------------------------

       -3      -15    -48   -240

multiply - 240 * 5 = -1200

add      

       -3      0      27         0     1200

5               -15   -75       -240 -1200

   ---------------------------------------------------

       -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

                 ------------------------------------------

I will skip the step by step

                       -3      -15    -48   -240  

  -5                            15    0      240

                 ------------------------------------------

                  - 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

hh