find a third degree polynomial function with real coefficients -2+i and -4 zeros

Answer 1

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Your conditions make no sense.

Did you mean -4 is a zero and -2+i is a zero ?

if so, then we can do this:
complex roots always come in conjugate pairs
so if -2+i is a zero, then -2-i is also a zero
using the sum and product properties
sum of those two roots = -2+i + -2-i = -4
product of those two roots = (-2+i)(-2-i)
= 4 - i^2 = 5
so the quadratic for the two complex roots is
x^2 +4x + 5

then your cubic would be
y = (x+4)(x^2 + 4x + 5)

expand if needed