1. Roots and Zeros
5.7

2. We know: the degree of the equation tells you the number of solutions
imaginary solutions come in pairs

5. New info:
if an imaginary number is a zero, then it’s conjugate is also a zero
so, if 3i is a solution, – 3i is also a solution

6. Writing polynomial functions from zeroes
Example 1:
Write a polynomial function of least degree that
has real coefficients and has the roots 3, 2, –4.

7. Example 2 Write a polynomial function of least
degree that has real coefficients and a
leading coefficient of 1 and has the
roots 1 and 5i.

8. Writing polynomial functions from zeroes
Example 3:
Write a polynomial function of least degree with integral coefficients, the zeros of which include -3, 2, and – 7i.