Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions.

Question

n=3

4 and 4i are zeros

f(1)=-153

Answer 1

imaginary zeros come in conjugate pairs. If 4i is a zero, so is -4i

then (x-4i) and (x+4i) are factors. Their product is x^2+4

the other factor is x-4. Multiply them together to get x^3-4x^2+4x -16

this would work except you need f(1) = -153, as it is, you would get f(1)= -15

to convert -15 to -153, multiply by 153/15 = 10.2 = 51/5

to get

f(x) = (51/5)(x^3 -4x^2 +4x -16) or

f(x) = 51x^2/5 - 204x^2/5 + 204x/5 - 816/5

f(1) = 51/5 -816/5 = - 153