Answer
See explanations.
Work Step by Step
Step 1. Given $f(x)=x^4-4x^3-x+3$, for $x=0.5$, we have $f(0.5)=(0.5)^4-4(0.5)^3-(0.5)+3=2.0625\gt0$
Step 2. For $x=1$, we have $f(1)=(1)^4-4(1)^3-(1)+3=-1\lt0$
Step 3. As $f(0.5)$ and $f(1)$ have opposite signs, based on the intermediate value theorem, there is a real zero between 0.5 and 1.