jmc

By the Rational Root Theorem, the only possible rational roots are of the form $\pm \frac{a}{b},$ where $a$ divides 21 and $b$ divides 2. Thus, the possible rational roots are $$\pm 1,\pm 3,\pm 7,\pm 21,\pm \frac{1}{2},\pm \frac{3}{2},\pm \frac{7}{2},\pm \frac{21}{2}.$$Checking these values, we find that the rational roots are $\boxed{-\frac{3}{2},-1,7}.$