Comment Its incomprehensible that a point of such importance Symmetry inflection the solutions and critical points evaluation isnt mentioned within whole article Moreover the circle at Figure  is unnecessary dislocated above SsyS omitting even a vertical line up to the center of the circle as done at Figure  of New approach  by Nickalls R W D see note  again  Tschirnhaus transformation isnt only unneeded but also responsible for such a failure hence tS    doesnt mean that an inflection point Sq doesnt exist It seems to me reasonable the unknown t along with the variables p and q to be abandoned in favour of graphically grounded ones which are also easier for memorizing