Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions.

Question

Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing​ utility, use it to graph the function and verify the real zeros and the given function value.

n=3

-4 and 7+2i

f(-1)=204



Answer 1

This one's fun. You have three roots: one is -4. That means you'll have a factor of (x - -4). The other is one of an imaginary root so you want something that allows for a root of 7+/- 2i. If you multiply those factors (x-7+2i) and (x-7-2i) you get x^2-14x+53. You need to check that f(-1)=204 so (-1+4)=3 and ((-1)^2+14+53)=68 so this multiples out to 204. Hope that helps.