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