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