Chapter 2 - Linear and Quadratic Functions - Section 2.7 Complex Zeros of a Quadratic Function* - 2.7 Assess Your Understanding - Page 178: 34

$-1,-3,\frac{1\pm i\sqrt {3}}{2},\frac{3\pm3i \sqrt {3}}{2}$

$P(z)=z^6+28z^3+27=(z^3+1)(z^3+27)=(z+1)(z^2-z+1)(z+3)(z^2-3z+9)$. Let $P(z)=0$, we get: 1. $z=-1,-3$ 2. $z=\frac{1\pm\sqrt {1-4}}{2}=\frac{1\pm i\sqrt {3}}{2}$ 3. $z=\frac{3\pm\sqrt {9-4(9)}}{2}=\frac{3\pm3i \sqrt {3}}{2}$