so my conjecture is true. So, the equation of a tangent at the mean of any two roots will intersect the x-axis at the third root. Real life example: Air weather is the feeling of weightlessness or negative gravitational pull experienced on a roller coaster or other ride. On roller coasters this sensation is usually achieved by the train going over a hill. Flight time is caused by the inertia of the train and passengers. As the train climbs a hill, the mass of travelers tends to resist the downward motion of the vehicle, causing passengers to briefly lift from their seats. The amount of flight time caused by a run depends on the speed of the train, gravity, and the transition radius of the track. Zero-G (meaning zero G-force) is achieved when the downward acceleration is equal to that of gravity, while negative G-forces are caused when the downward acceleration is greater than that of gravity.