Write a polynomial function of degree 7 that has the given zeros : 6 multiplicity 3,-4i, i

Hello from MrBillDoesMath!

x^7 - 18 x^6 + 125 x^5 - 522 x^4 + 1852 x^3 - 3960 x^2 + 1728 x - 3456

See Discussion for details.

Discussion:

The polynomial is

(x-6)^3 * (x-4i)(x+4i)(x-i)(x+i)   =

x^7 - 18 x^6 + 125 x^5 - 522 x^4 + 1852 x^3 - 3960 x^2 + 1728 x - 3456

Thank you,

MrB

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph