  The A-polynomial of a knot in S^3 defines a complex plane curve associated to
the set of representations of the fundamental group of the knot exterior into
SL(2,C). Here, we show that a non-trivial knot in S^3 has a non-trivial
A-polynomial. We deduce this from the gauge-theoretic work of Kronheimer and
Mrowka on SU_2-representations of Dehn surgeries on knots in S^3. As a
corollary, we show that if a conjecture connecting the colored Jones
polynomials to the A-polynomial holds, then the colored Jones polynomials
distinguish the unknot
