Problem

2. Given that $x = -\dfrac{1}{3}$ is a root of the equation

$3x^3 + kx^2 + 33x + 13 = 0 \quad k \in \mathbb{R}$

determine

(a) the value of $k$,

(b) the other 2 roots of the equation in the form $a + ib$, where $a$ and $b$ are real numbers.