By Descartes' Rules of Signs, you need to find the sign changes for f(x) and f(-x) [Positive and Negative Case - respectively]
f(x) = 8x^4 + 13x³ - 11x² + x + 9
Since there are two sign changes between terms, we can show that there are possibly 2 positive roots.
f(-x) = 8x^4 - 13x³ - 11x² - x + 9
For the negative case, you let x = -x. Then, we have 8x^4 - 13x³ - 11x²
- x + 9. There are 2 possible negative roots since there are 2 sign
changes. Hence, the possible choice is:
Positive Real: 2 or 0
Negative Real: 2 or 0
Complex: 4, 2 or 0
i know i am late and i hope you still need the help ! :D
