Question Number 210559 by mathlove last updated on 12/Aug/24
![deg [p(x^2 )∙q(x)]=20 deg[((p(x)^3 )/(q(x)^2 ))]=2 then deg q(x)=?](https://www.tinkutara.com/question/Q210559.png)
$${deg}\:\left[{p}\left({x}^{\mathrm{2}} \right)\centerdot{q}\left({x}\right)\right]=\mathrm{20} \\ $$$${deg}\left[\frac{{p}\left({x}\right)^{\mathrm{3}} }{{q}\left({x}\right)^{\mathrm{2}} }\right]=\mathrm{2} \\ $$$${then}\:{deg}\:\:{q}\left({x}\right)=? \\ $$
Answered by mr W last updated on 12/Aug/24
$${say}\:{deg}\:{p}\left({x}\right)={m},\:{deg}\:{q}\left({x}\right)={n} \\ $$$$\mathrm{2}{m}+{n}=\mathrm{20} \\ $$$$\mathrm{3}{m}−\mathrm{2}{n}=\mathrm{2} \\ $$$$\Rightarrow{m}=\mathrm{6},\:{n}=\mathrm{8} \\ $$$${i}.{e}.\:{deg}\:{p}\left({x}\right)=\mathrm{6},\:{deg}\:{q}\left({x}\right)=\mathrm{8} \\ $$
Commented by mathlove last updated on 12/Aug/24
$${thanks} \\ $$