Odd Prime Cubic Root

Consider the general cubic polynomial with nonzero integer coefficients and constant term, namely, $f(x) = ax^3 +bx^2 +cx +d$ where $a>2$ is prime, $|d|>2$ is prime, and $f(1) = a+d\neq0$ . From the given info above, $c = -b$ . Find another expression of $c$ that proves $f(x)$ has root $x=-1$ .