3.2: Modulus quadratic graph and cubic with consecutive roots

The diagram shows the graph of $y = \lvert f(x) \rvert$, where $f(x)$ is a quadratic function. Write down the two possible expressions for $f(x)$.

The three roots of $p(x) = 0$, where $p(x) = 5x^{3} + ax^{2} + bx - 2$, are $x = \dfrac{1}{5}$, $x = n$ and $x = n + 1$, where $a$ and $b$ are positive integers and $n$ is a negative integer. Find $p(x)$, simplifying your coefficients.