Question Number 53502 by 0955083339 last updated on 22/Jan/19
$$\mathrm{If}\:\left({x}−\mathrm{5}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{factor}\:\mathrm{of}\:\:\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{px}−\mathrm{2}{p}=\mathrm{0}, \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\:{p}\:\:\mathrm{is} \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 22/Jan/19
$$\mathrm{2}×\mathrm{5}^{\mathrm{2}} +\mathrm{2}{p}×\mathrm{5}−\mathrm{2}{p}=\mathrm{0} \\ $$$$\mathrm{50}+\mathrm{10}{p}−\mathrm{2}{p}=\mathrm{0} \\ $$$${p}=\frac{−\mathrm{50}}{\mathrm{8}}=\frac{−\mathrm{25}}{\mathrm{4}} \\ $$
Answered by afachri last updated on 22/Jan/19
$$\mathrm{2}\left(\mathrm{5}\right)^{\mathrm{2}} +\:\mathrm{2}\boldsymbol{{p}}\left(\mathrm{5}\right)\:−\:\mathrm{2}\boldsymbol{{p}}\:\:\:\:=\:\:\:\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{50}\:+\:\mathrm{10}\boldsymbol{{p}}\:−\:\mathrm{2}\boldsymbol{{p}}\:\:=\:\:\:\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{8}\boldsymbol{{p}}\:\:=\:\:−\mathrm{50} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{p}}\:\:=\:−\:\frac{\mathrm{50}}{\mathrm{8}}\:=\:−\mathrm{6}\frac{\mathrm{1}}{\mathrm{4}} \\ $$