CGMO 2007 Problem 7

Let $a$ , $b$ , $c$ be integers each with absolute value less than or equal to $10$ . The cubic polynomial $f(x) = x^3 + ax^2 + bx + c$ satisfies the property $$\Big|f\left(2 + \sqrt 3\right)\Big| < 0.0001.$$ Determine if $2 + \sqrt 3$ is a root of $f$ .