Solution:
\( \displaylines{\text{If }\frac{p}{q}\text{ is a root, then }p\left|6\text{ and }q\right|4,\text{ so all possible roots include factors such as }\\ p=1,2,3,6\\ q=1,2,4\\ \text{yielding a list:}\\ \frac{p}{q}=\pm1,\pm2,\pm3,\pm6,\pm\frac12,\pm\frac32,\pm\frac14,\pm\frac34} \)