Answer
See table.
Work Step by Step
Step 1. Given $f(x)=6x^4+2x^3+9x^2+x+5$, we can identify 0 sign change indicating that there will be no positive zeros. Put the numbers in the table.
Step 2. $f(-x)=6x^4-2x^3+9x^2-x+5$, we can identify 4 sign changes indicating that there could be 4, 2, or 0 negative zeros. Put the numbers in the table.
Step 3. There should be 4 total zeros. thus the number of nonreal zeros will be the remaining after taking real zeros into account. Complete the table as shown.