Copy of Determine quintic by 3 stationary points
In the applet Michael Borcherds is a great way to use CAS! Here you can find the fourth critical point too.
Add to the CAS applet
45: Division(ff'(g), (g-a) (g-b) (g-c)); 46: Solve(Element(45,1),g);47: ff(Element($46,1)) = h
g = (-5 A a - 5A b - 5A c - 4B)/(5A); h = A g⁵ + B g⁴ + C g³ + D g² + E g + F ⇒ P_4 = (g, h)
another critical point.