UNsolving Polynomial Equations

UNsolving an equation means choosing a solution set and then finding an equation that has that solution set. In the left hand panel you can choose the order of the polynomial equation you want to UNsolve. By dragging the GREEN dots you can choose a solution set. The right hand panel will then show an equation with that solution set. Dragging the RED dot in the right hand panel will allow you to see other equations with the same solution set. For a given solution set, how many equations or inequalities are there that have that solution set? How do you know? Can you prove it?