Answer
See table.
Work Step by Step
Step 1. Given $f(x)=5x^6-6x^5+7x^3-4x^2+x+2$, we can identify 4 sign changes indicating that there could be 4, 2 or 0 positive zeros. Put the numbers in the table.
Step 2. $f(-x)=5x^6+6x^5-7x^3-4x^2-x+2$, we can identify 2 sign changes indicating that there could be 2 or 0 negative zeros. Put the numbers in the table.
Step 3. There should be 6 total zeros. thus the number of nonreal zeros will be the remaining after taking real zeros into account. Complete the table as shown.