Chapter 2 - Linear and Quadratic Functions - Section 2.7 Complex Zeros of a Quadratic Function* - 2.7 Assess Your Understanding - Page 178: 33

$1,2, \frac{-1\pm i\sqrt {3}}{2}, -1\pm i\sqrt 3$

$F(x)=x^6-9x^3+8=(x^3-1)(x^3-8)=(x-1)(x^2+x+1)(x-2)(x^2+2x+4)$. Let $F(x)=0$, we get: 1. $x=1,2$ 2. $x=\frac{-1\pm\sqrt {1-4}}{2}=\frac{-1\pm i\sqrt {3}}{2}$ 3. $x=\frac{-2\pm\sqrt {4-4(4)}}{2}=-1\pm i\sqrt 3$