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!