SOLUTION: I NEED HELP WITH THE FOLLOWING QUESTION: Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing​ utility

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I NEED HELP WITH THE FOLLOWING QUESTION: Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing​ utility      Log On


   

Question 1162143: I NEED HELP WITH THE FOLLOWING 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 2 and
2i are zeros f(-1)=-15
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

If R is a zero then (x-R) is a factor
If A+Bi is a zero, and the coefficients are real numbers, then A-Bi is
also a solution.
There is always a constant k which is a factor (it may be 1 understood but
it may not be)

f(x) = k(x-2)(x-2i)(x+2i)
f(x) = k(x-2)(x²-4i²)
f(x) = k(x-2)(x²-4∙-1)
f(x) = k(x-2)(x²+4)
f(x) = k(x³+4x-2x²-8)
f(x) = k(x³-2x²+4x-8)
f(-1) = k[(-1)³-2(-1)²+4(-1)-8] = -15
                 k[-1-2(1)-4-8] = -15
                    k[-1-2-4-8] = -15
                         k[-15] = -15
                              k = 1
f(x) = 1(x³-2x²+4x-8)
f(x) = x³-2x²+4x-8        <--final answer

Here's the graph.  Scroll down to see it all.




Edwin