A

Step 1: To find the net force acting on the system, we start by calculating the force from the potential energy function. The force $F$ in a conservative force field is given by the negative gradient of the potential energy:
$$ F = -\frac{dU}{dx} $$
Given the potential energy function: $$ U = ax^2 - bx $$, we differentiate it with respect to $x$:
$$ F = -\frac{d}{dx}(ax^2 - bx) = - (2ax - b) = b - 2ax. $$
Setting the force to zero for equilibrium conditions gives:
$$ b - 2ax = 0 \implies 2ax = b \implies x = \frac{b}{2a}. $$
Step 2: For stability of the equilibrium, we examine the second derivative of the potential energy.
Calculation of the second derivative:
$$ F = b - 2ax \implies \frac{dF}{dx} = -2a. $$
Since $-2a < 0$ for $a > 0$, the equilibrium is stable.
Step 3: The potential energy at the equilibrium position $x = \frac{b}{2a}$ is given by substituting this value back into the potential energy function:
$$ U_{eq} = a\left(\frac{b}{2a}\right)^2 - b\left(\frac{b}{2a}\right) = \frac{ab^2}{4a^2} - \frac{b^2}{2a} = \frac{b^2}{4a} - \frac{2b^2}{4a} = -\frac{b^2}{4a}. $$
Thus, matching the answers from Column II, we see:
(i) Force: $\frac{b}{2a}$ (matches with A)
(ii) Equilibrium Position: $b - 2ax$ (matches with B)
(iii) Potential Energy: $-\frac{b^2}{4a}$ (matches with C)
(iv) Equilibrium: stable (matches with D)
Therefore, the answer regarding the net force acting on the system is option [A] = \frac{b}{2a}.
Therefore, A.