SOLUTION: Find a fourth degree polynomial function f(x) having only real coefficients,-1,4, and i as zeros, and f(2)=30

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find a fourth degree polynomial function f(x) having only real coefficients,-1,4, and i as zeros, and f(2)=30      Log On


   

Question 375885: Find a fourth degree polynomial function f(x) having only real coefficients,-1,4, and i as zeros, and f(2)=30
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
If x=i is a solution, then so is x=-i since complex solutions only come in complex conjuate pairs.
f%28x%29=a%28x-1%29%28x-4%29%28x-i%29%28x%2Bi%29
f%28x%29=a%28x-1%29%28x-4%29%28x%5E2%2B1%29
.
.
f%282%29=a%282-1%29%282-4%29%282%5E2%2B1%29=30
a%281%29%28-2%29%285%29=30
a=-3
.
.
.
highlight%28f%28x%29=-3%28x-1%29%28x-4%29%28x%5E2%2B1%29%29