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

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1