SOLUTION: Find an nth degree polynomial function with real coefficients satisfying the given conditions. n=3; 3 and i are zeros; f(2)=10

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find an nth degree polynomial function with real coefficients satisfying the given conditions. n=3; 3 and i are zeros; f(2)=10      Log On


   

Question 317254: Find an nth degree polynomial function with real coefficients satisfying the given conditions.
n=3; 3 and i are zeros; f(2)=10
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Since i is a root, then -i is also a root since complex roots only occur in complex conjugate pairs.
.
.
.
f%28x%29=A%28x-i%29%28x%2Bi%29%28x-3%29
f%28x%29=A%28x%5E2%2B1%29%28x-3%29
.
.
Use the point to solve for A.
.
.
f%282%29=A%284%2B1%29%282-3%29=10
A%285%29%28-1%29=10
A=-2
.
.
.
f%28x%29=-2%28x%5E2%2B1%29%28x-3%29
f%28x%29=-2%28x%5E3-3x%5E2%2Bx-3%29