### Home > PC3 > Chapter 12 > Lesson 12.1.1 > Problem12-15

12-15.

Write an equation for a fifth-degree polynomial function that has roots of $x = 5$ and $x = \frac { 3 + 2 i } { 2 }$, a double root of $x = −3$, and passes through the point $(1, −8)$.

If $x=\frac{3+2i}{2}$ is a root, then $x=\frac{3-2i}{2}$ is also a root.

If $x=\frac{3+2i}{2}$ is a root, then $(2x-3-2i)$ is the corresponding factor.