### Home > PC3 > Chapter 11 > Lesson 11.1.3 > Problem11-43

11-43.

Write an equation for a sixth-degree polynomial function that has roots of $x = −2 ±\sqrt { 3 }$, a double root at $x = 0$, a complex root of $x = 5 + 3i$, and passes through the point $(−1, −12)$.

$p(x) = a(x-(2+\sqrt{3}))(x-(2-\sqrt{3}))(x-0)^2(x-(5 + 3i))(x-(5 - 3i))$