Copy of Determine quintic by 3 stationary points

In the [url=https://www.geogebra.org/m/jc3hpzrd]applet [/url] Michael Borcherds is a great way to use CAS! Here you can find the fourth critical point too.[br]Add to the CAS applet[br]45: Division(ff'(g), (g-a) (g-b) (g-c)); 46: Solve(Element(45,1),g);47: ff(Element($46,1)) = h[br]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)[br]another critical point.
Derivation (using CAS)

Information: Copy of Determine quintic by 3 stationary points