This problem can be solved easily by using Table. Please see the documentation on Table for examples of how to use it.
pointList = Table[
A = x^3 + 3;
B = 3 x;
Equation = z^2 + A*z + B;
V1 = Re[Root[Equation, 1]];
{x, V1}, {x, 0.1, 10, 0.1}]
You can then use ListPlot on the result:
ListPlot[pointList]