Question Number 65959 by ajfour last updated on 06/Aug/19
$${x}^{\mathrm{5}} +{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$$$\left({x}^{\mathrm{2}} +{px}+{q}\right)\left({x}^{\mathrm{3}} +{rx}^{\mathrm{2}} +{sx}+{t}\right)=\mathrm{0} \\ $$$${then}\:{elimating}\:{r},{s},{t}\: \\ $$$$\:{pq}\left({p}^{\mathrm{2}} +{a}\right)+{d}={q}\left({b}+\mathrm{2}{pq}\right) \\ $$$$\:{q}^{\mathrm{2}} \left({p}^{\mathrm{2}} +{a}\right)+{dp}={q}\left({c}+{q}^{\mathrm{2}} \right) \\ $$$${please}\:{try}\:{bringing}\:{into}\:{single} \\ $$$${variable}\:{sir}… \\ $$$$\: \\ $$