SOLUTION: 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 th

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 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 th      Log On


   

Question 1167254: 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 6+4i are zeros
f(-1)=65
Answer by josgarithmetic(39627) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B2%29%28x-%286%2B4i%29%29%28x-%286-4i%29%29
%28x%2B2%29%28%28x-6%29-4i%29%28%28x-6%29%2B4i%29
%28x%2B2%29%28%28x-6%29%5E2-16%2A-1%29
%28x%2B2%29%28x%5E2-12x%2B36%2B16%29
highlight%28%28x%2B2%29%28x%5E2-12x%2B52%29%29

for function f, need some factor k which is found when x=-1.
f%28-1%29=k%28-1%2B2%29%28%28-1%29%5E2-12%28-1%29%2B52%29=65
.
.
k=1
.