SOLUTION: Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions. n=3 3 and 5i are zeros f(-1)=104 f(x)=???

Algebra ->  Rational-functions -> SOLUTION: Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions. n=3 3 and 5i are zeros f(-1)=104 f(x)=???      Log On


   

Question 1128103: Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions.
n=3
3 and 5i are zeros
f(-1)=104
f(x)=???
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

n=3=> 3rd degree
zeros:
x%5B1%5D=3
x%5B2%5D=+5i -> complex zeros always come in pairs, so you also have
x%5B3%5D=+-5i
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29
f%28x%29=%28x-3%29%28x-5i%29%28x%2B5i%29
f%28x%29=%28x-3%29%28x%5E2-%285i%29%5E2%29
f%28x%29=%28x-3%29%28x%5E2-25i%5E2%29
f%28x%29=%28x-3%29%28x%5E2-25%28-1%29%29
f%28x%29=%28x-3%29%28x%5E2%2B25%29
f%28x%29=x%5E3%2B25x-3x%5E2-75
f%28x%29=x%5E3-3x%5E2%2B25x-75


is f%28-1%29=104?
f%28-1%29=%28-1%29%5E3-3%2A%28-1%29%5E2%2B25%28-1%29-75
f%28-1%29=-1-3-25-75
f%28-1%29=-104
so, f%28-1%29=104 is not true