Instead of doing your homework for you, I will do one exactly like yours
step-by-step only with slightly different numbers. I'll do this one instead:
Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 5; zeros: -5; -2i; -4+2i
If a polynomial has a complex imaginary zero a+bi, then a-bi is also a zero.
So all the zeros are: -5; -2i; +2i; -4+2i; -4-2i
Set x equal to each:
x = -5; x = -2i; x = +2i; x = -4+2i; x = -4-2i
Get 0 on the right of each:
x+5 = 0; x+2i = 0; x-2i = 0; x+4-2i = 0; x+4+2i = 0
Multiply all the left and right sides together:
So a polynomial function of degree 5 which we must set = 0, to find
the zeros: -5; -2i; -4+2i is the left side of the preceding equation:
Edwin
