Sketch the graph of any cubic function that has three distinct real roots and a positive coefficient of $x^3$.

A research team models the potential energy $V$ of a chemical system as a function of its configuration $x$ using the equation

where $a$ and $k$ are constants and $a>0$.

Verify that the energy profile has a stationary point where it intersects the vertical $V$-axis.

Given that the equation $V(x)=0$ has three distinct real roots, determine the range of possible values for $k$ in terms of $a$ by considering the nature and positions of the local maximum and local minimum points.