Answer
$x=-\frac{1}{2}, 1, 2$
Work Step by Step
Step 1. As $2$ is a zero of $f(x)$, we can try to divide $f(x)$ by $x-2$
Step 2. The coefficients of the dividend $f(x)$ can be identified in order as $\{2,-5,1,2\}$ and the divisor is $x-2$; use synthetic division as shown in the figure to get the quotient and the remainder.
Step 3. We can identify the result as $f(x)=(2x^2-x-1)(x+1)=(2x+1)(x-1)(x-2)$; thus we can find the zeros of $f(x)$ as $x=-\frac{1}{2}, 1, 2$
