degree 4; zeros:-5-3i; -5 multiplicity 2

Question

form of polynomial

Answer 1

The single complex zero needs to be counterbalanced by another complex zero to make coefficients of the fourth degree polynomial real. The other complex zero has value -5+3i. The polynomial is the product of all the factors:

(x+5+3i)(x+5-3i)(x+5)^2⇒(x^2+10x+34)(x^2+10x+25)

⇒x^4+10x^3+25x^2+10x^3+100x^2+250x+34x^2+340x+850⇒

x^4+20x^3+159x^2+590x+850