SOLUTION: Find an nth-degree polynomial function with real coefficients satisfying the given conditions. n=4; i and 4i are zeros;f(-1)=68

Algebra ->  College  -> Linear Algebra -> SOLUTION: Find an nth-degree polynomial function with real coefficients satisfying the given conditions. n=4; i and 4i are zeros;f(-1)=68      Log On


   

Question 370092: Find an nth-degree polynomial function with real coefficients satisfying the given conditions. n=4; i and 4i are zeros;f(-1)=68
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
If i and 4i are zeros so are -i and -4i
f%28x%29=a%28x-i%29%28x%2Bi%29%28x-4i%29%28x%2B4i%29
f%28x%29=a%28x%5E2%2B1%29%28x%5E2%2B16%29
.
.
Solve for a.
f%28-1%29=a%281%2B1%29%281%2B16%29=68
a%2834%29=68
a=2
.
.
f%28x%29=2%28x%5E2%2B1%29%28x%5E2%2B16%29
f%28x%29=2%28x%5E4%2B16x%5E2%2Bx%5E2%2B16%29
highlight%28f%28x%29=2x%5E4%2B34x%5E2%2B32%29