Answer
4, 2, or 0 positive real zeros.
1 negative real zero.
Work Step by Step
Step 1. For $f(x)=12x^8-x^7+8x^4-2x^3+x+3$, we can find 4 sign changes indicating that there may be 4, 2, or 0 positive real zeros.
Step 2. For $f(-x)=12x^8+x^7+8x^4+2x^3-x+3$, we can find 1 sign change indicating that there will be 1 negative real zero.