Chapter 3 - Section 3.5 - Complex Zeros and the Fundamental Theorem of Algebra - 3.5 Exercises - Page 294: 57

$1,\pm2i,\pm\sqrt 3i$

1. List possible rational zeros $\pm1,\pm2,\pm3,\pm4,\pm6,\pm12$ 2. Use synthetic division or remainder theorem to test some of the values. 3. We can find one rational zero at $x=1$ and the quotient as shown $P(x)=(x-1)(x^4+7x^2+12)=(x-1)(x^2+4)(x^2+3)$ 4. Solve the quadratic terms, we have all the zeros as $1,\pm2i,\pm\sqrt 3i$