posted by Bella .
form a polynomialf(x) with real coefficients, having the given degree and zeros
degree 5; zeros -5;-i; -5+i
If x = -i and x = -5 +i are roots, so must be x = i and x = -5 -i.
is a polynomial with those roots, where A is any constant.
Let's set A = 1.
That can be rewritten
(x+5)(x^2 +1)(x^2 +10x +25 +1)= 0
(x^3 +5x^2 +x +5)(x^2 +10x +26) = 0
Multiply that out for the full fifth order polynomial.