Answer
$\{\frac{1}{2},2,2,5\}$
Work Step by Step
Step 1. Given $f(x)=2x^4-19x^3+57x^2-64x+20$, list possible rational zeros as $\frac{p}{q}=\pm1,\pm2,\pm4,\pm5,\pm10,\pm20,\pm\frac{1}{2},\pm\frac{5}{2}$
Step 2. Use synthetic division as shown in the figure to find zero(s) $x=2,5$.
Step 3. Use the quotient and solve $2x^2-5x+2=0$ or $(x-2)(2x-1)=0$, thus $x=\frac{1}{2}, 2$.
Step 4. Thus the real zeros are $\{\frac{1}{2},2,2,5\}$
