Answer
$x=-4, -\frac{1}{2}, x= 2$ (multiplicity 2).
Work Step by Step
Step 1.For $2x^4+x^3-24x^2+20x+16=0$, list possible rational real zeros $\frac{p}{q}: \pm1,\pm2,\pm4,\pm8,\pm16,\pm\frac{1}{2}$
Step 2. Use synthetic division as shown in the figure to find zero(s) $x=-4,2$
Step 3. Use the quotient to find other zeros: $2x^2-3x-2=0 \Longrightarrow (2x+1)(x-2)=0 \Longrightarrow x=-\frac{1}{2}, 2$
