A Constant from Three Zeros

Let $f(x)=x^3+ax^2+b$ ($a,b\in\mathbb R$).

1. Discuss the monotonicity of $f(x)$. 2. Suppose $b=c-a$, where $c$ is a constant independent of $a$. If the set of values of $a$ for which $f(x)$ has three distinct zeros is exactly $(-\infty,-3)\cup\left(1,\dfrac 32\right)\cup\left(\dfrac 32,+\infty\right)$, find $c$.