2.9: Polynomial from given roots

The three roots of $p(x) = 0$, where $p(x) = 2x^{3} + ax^{2} + bx + c$ are $x = \tfrac{1}{2}$, $x = n$ and $x = -n$, where $a$, $b$, $c$ and $n$ are integers. The $y$-intercept of the graph of $y = p(x)$ is 4. Find $p(x)$, simplifying your coefficients.