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 v

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 v      Log On


   

Question 1042147: 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 1+2i are zeros
f(2)=30
f(x)=
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=a%28x%2B4%29%28x-%281%2B2i%29%29%28x-%281-2i%29%29, a is unknown factor, determinable later using x=2.

f%28x%29=a%28x%2B4%29%28x-1-2i%29%28x-1%2B2i%29
f%28x%29=a%28x%2B4%29%28%28x-1%29-2i%29%28%28x-1%29%2B2i%29
a%28x%2B4%29%28x%5E2-2x%2B1-4%28-1%29%29
highlight%28f%28x%29=a%28x%2B4%29%28x%5E2-2x%2B5%29%29

FINDING FACTOR a
f%282%29=30 as given
a%282%2B4%29%282%5E2-2%2A2%2B5%29=30
a%2A6%2A5=30
a=1

THE FUNCTION f
highlight%28f%28x%29=%28x%2B4%29%28x%5E2-2x%2B5%29%29
Do the multiplication to put into general polynomial form.