# college alg

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form a polynomialf(x) with real coefficients, having the given degree and zeros

degree 5; zeros -5;-i; -5+i

• college alg -

If x = -i and x = -5 +i are roots, so must be x = i and x = -5 -i.
A(x+5)(x-i)(x+i)(x+5+i)(x+5-i)= 0
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
or
(x^3 +5x^2 +x +5)(x^2 +10x +26) = 0

Multiply that out for the full fifth order polynomial.

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