I have been playing around with some geogebra and noticed this and i can't see if it is general or not...

Take any cubic equation with a turning points and find its three points of intersection with a line ( i.e. line cuts through the curve in 3 places). If i sum of the x values of the points of intersection , it comes to a number , say p. If i then move the line to another place by messing with its gradient or intercept ( where it still cuts in 3 places), the sum of the x values is p again!

Does this make any sense?