Write a polynomial function if its leading coefficient is -3, and its roots include 4, 0 and 5x-2i.

Step-by-step explanation:

Complex roots come in conjugates.  Your roots are

x = -3i

x= 3i

x = 2

x = -i

x = i

Since  i=√-1 , then i2=-1

For the root   x = 3i , we can say that the factor is  

(x - 3i)(x + 3i) = x2 - 9i2

                     = x2 - 9(-1)

                     = x2 + 9

(x - i)(x + i) = x2 - i2

                 = x2 + 1

Then your polynomial is

f(x) = (x - 2)(x2 + 1)(x2 + 9)

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!