SOLUTION: N=3; 2 and 2i are zeros; f(-1)=15

Algebra ->  Rational-functions -> SOLUTION: N=3; 2 and 2i are zeros; f(-1)=15      Log On


   

Question 1067436: N=3; 2 and 2i are zeros; f(-1)=15
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
if 2i is a root, so is -2i
(x-2i)(x+2i)(x-2)
x^2-4i^2=(x^2+4) (x-2) are factors
x^3-2x^2+4x-8=0
We know that (-1,15) is a point
so a[(-1)-2-4-8]=15
so that a(-15)=15
a=-1
-x^3+2x^2-4x+8 is the polynomial
graph%28300%2C300%2C-10%2C10%2C-30%2C30%2C-x%5E3%2B2x%5E2-4x%2B8%29