Smallest polynomial with given roots
Algebra
Level
3
Let \( f(x) \) be a monic polynomial with real coefficients such that \( 2\) and \( 1+i\) are both roots of \( f.\) Suppose that \( f\) has the smallest possible degree given these requirements. What is \( f(3)?\)
Clarification: \(i=\sqrt{-1}\).
by
Patrick Corn