Question

Write a polynomial function in standard form with real coefficients whose zeros include 2 comma 7 i comma and negative 7 i .

Answer 1

This will be a third degree polynomial since we have 3 zeros.  We will FOIL them out.  They are: (x-2), (x+7i), (x-7i).  The product of the second and third factors gives us $x^2-49i^2$.  i^2 = -1, so if we simplify, we have $x^2-49(-1)=x^2+49$.  Now we will multiply that with x-2 to get $x^3-2x^2+49x-98$.  There you go!