SOLUTION: Find a third degree polynomial f(x), which has roots 2, 1-2i and which has y-intercept 2 (ie, f(0) =2).

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find a third degree polynomial f(x), which has roots 2, 1-2i and which has y-intercept 2 (ie, f(0) =2).      Log On


   

Question 133139: Find a third degree polynomial f(x), which has roots 2, 1-2i and which has y-intercept 2 (ie, f(0) =2).
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
You are given two root. One of those roots is imaginary. So there is another imaginary root.
roots are 2, 1-2i, 1+2i
f%28x%29+=+%28x-2%29+%28x+-+%281-2i%29%29+%28x+-+%281%2B2i%29+%29
multiply to get
+f%28x%29+=+%28x-2%29%28x%5E2+-2x+%2B3%29+
What is f(0)?
f%280%29+=+%28-2%29%283%29 = -6
We want f(0) to be 2. So we need to divide our function by -3.
f%28x%29+=+-%28%28x-2%29%28x%5E2+-2x+%2B3%29%29%2F3+