Answer
2 or 0 positive real zeros.
2 or 0 negative real zeros.
Work Step by Step
Step 1. Given the function $f(x)=2x^4-5x^3-x^2-6x+4$, we can see that $f(x)$ has 2 sign changes. Thus, based on Descartes’s Rule of Signs, the function may have 2 or 0 positive real zeros.
Step 2. Testing the function $f(-x)=2x^4+5x^3-x^2+6x+4$, we can see that $f(-x)$ has 2 sign changes. Thus, based on Descartes’s Rule of Signs, the function may have 2 or 0 negative real zeros.
