Find the 4 degree polynomial with zeros at x= 1, x= -4, and x= 2 -2 i; f(0)=- 96

3x^4 - 3x^3 - 24x^2 + 120x - 96

Step-by-step explanation:

When we approach one of these problems, we should try to write out an equation as if it were factored.

f(x) = a(x-1)(x+4)(x-2+2i)(x-2-2i)

note here that a is a constant we can solve for later. and I added the last root on since whenever we have 1 complex root, it's conjugate is also a complex root.

expanding this we obtain

f(x) = a(x^4 - x^3 - 8x^2 + 40x - 32)

we want f(0) = -96

what value of a would make the term with no variable attached equal to -96?

-32 × 3 = -96

so a =3 and our final answer is

3x^4 - 3x^3 - 24x^2 + 120x - 96

14.3

step-by-step explanation:

add all the numbers together.

9 + 12 + 15 + 16 + 17 + 17 = 86

now, divide 86 by how many numbers we have: 6.

86 / 6 = 14.3