Question Number 69143 by ajfour last updated on 20/Sep/19
![x^4 +ax^3 +bx^2 +cx+d=0 let x=f(t) linear perhaps t^4 +At^3 +Bt^2 +Ct+D=0 can we have 4AB=A^3 +8C solving at most a degree three polynomial ?](https://www.tinkutara.com/question/Q69143.png)
$${x}^{\mathrm{4}} +{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$$${let}\:\:{x}={f}\left({t}\right)\:\:{linear}\:{perhaps} \\ $$$${t}^{\mathrm{4}} +{At}^{\mathrm{3}} +{Bt}^{\mathrm{2}} +{Ct}+{D}=\mathrm{0} \\ $$$${can}\:{we}\:{have}\:\: \\ $$$$\:\:\:\mathrm{4}{AB}={A}^{\mathrm{3}} +\mathrm{8}{C}\:\:{solving}\:{at}\:{most} \\ $$$${a}\:{degree}\:{three}\:{polynomial}\:? \\ $$