### Home > PC3 > Chapter 6 > Lesson 6.1.1 > Problem6-23

6-23.

Write an equation for a fifth-degree polynomial function that has roots at  $x=-3\pm\sqrt{5}$, $x=−2$, $x=1$, $x=5$, and passes through the point $\left(−3, 20\right)$.

$p\left(x\right)=a\left(x-\left(-3+\sqrt{5}\right)\right)\left(x-\left(-3-\sqrt{5}\right)\right)\left(x-1\right)\left(x-5\right)$