Theorems about Roots of Polynomial Equations
Irrational and Imaginary Root Theorem
Example:
Find two additional roots for each.
a) 1  3 and  11
b) 2  7 and
5
c) 3 – i and 2i
d) 3i and -2 + i
Example:
Model:
a) Find a third degree polynomial equation with rational coefficients that has roots 3 and 1 + i.
b) Find a third degree polynomial equation with rational coefficients that has roots -1 and
7.
c) Find a fourth degree polynomial equation with rational coefficients that has roots 2  3 and 5 - 2i.