Author: Tinku Tara

Question Number 200353 by faysal last updated on 17/Nov/23 $$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{x}^{\mathrm{3}} +\mathrm{3px}^{\mathrm{2}} +\mathrm{3qx}+\mathrm{r}=\mathrm{0}\:\mathrm{are} \\ $$$$\mathrm{in}\:\mathrm{harmonic}\:\mathrm{progression},\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{2q}^{\mathrm{3}} =\mathrm{r}\left(\mathrm{3pq}−\mathrm{r}\right) \\ $$ Answered by jabarsing last updated on…

Question Number 200351 by faysal last updated on 17/Nov/23 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{x}^{\mathrm{3}} −\mathrm{12x}^{\mathrm{2}} −\mathrm{6x}−\mathrm{10}=\mathrm{0}\: \\ $$$$\mathrm{by}\:\mathrm{cardon}'\mathrm{s}\:\mathrm{method} \\ $$ Answered by Frix last updated on 17/Nov/23 $$\mathrm{The}\:\mathrm{name}\:\mathrm{is}\:{Cardano} \\…

Question Number 200336 by faysal last updated on 17/Nov/23 Answered by cortano12 last updated on 17/Nov/23 $$\:\:\begin{array}{|c|c|c|}{}&\hline{\mathrm{1}}&\hline{\mathrm{2}}&\hline{−\mathrm{3}}&\hline{\mathrm{5}}&\hline{−\mathrm{2}}&\hline{\mathrm{3}}\\{\mathrm{x}=\mathrm{2}}&\hline{\ast}&\hline{\mathrm{2}}&\hline{\mathrm{8}}&\hline{\mathrm{10}}&\hline{\mathrm{30}}&\hline{\mathrm{56}}\\{}&\hline{\mathrm{1}}&\hline{\mathrm{4}}&\hline{\mathrm{5}}&\hline{\mathrm{15}}&\hline{\mathrm{28}}&\hline{\mathrm{59}}\\\hline\end{array} \\ $$$$\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{is}\:\mathrm{59} \\ $$$$\mathrm{the}\:\mathrm{quotient}\:\mathrm{is}\:\mathrm{h}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{4}} +\mathrm{4x}^{\mathrm{3}} +\mathrm{5x}^{\mathrm{2}} +\mathrm{15x}+\mathrm{28} \\…