Answer
$\{-\frac{1}{2},2,4\}$
Work Step by Step
Step 1. Given $f(x)=2x^3-11x^2+10x+8$, list possible rational zeros as $\frac{p}{q}=\pm1,\pm2,\pm4,\pm8\pm\frac{1}{2}$
Step 2. Use synthetic division as shown in the figure to find a zero $x=2$.
Step 3. Use the quotient and solve $2x^2-7x-4=0$ or $(2x+1)(x-4)=0$, thus $x=-\frac{1}{2}, 4$.
Step 4. Thus the real zeros are $\{-\frac{1}{2},2,4\}$
