Question Number 161558 by Rasheed.Sindhi last updated on 19/Dec/21
$${What}'{s}\:{the}\:{value}\:{of}\:{a}\:{for}\:{which} \\ $$$${x}^{\mathrm{2}} +{x}={a}\:\&\:{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}={a}\:{have}\:{one} \\ $$$${root}\:{common}? \\ $$
Answered by MJS_new last updated on 19/Dec/21
$$\mathrm{we}'\mathrm{ve}\:\mathrm{got}\:\mathrm{2}\:\mathrm{equations}\:\mathrm{for}\:\mathrm{2}\:\mathrm{unknowns},\:\mathrm{just} \\ $$$$\mathrm{solve}\:\mathrm{the}\:\mathrm{system} \\ $$$$\left(\mathrm{1}\right)\:{x}^{\mathrm{2}} +{x}−{a}=\mathrm{0} \\ $$$$\left(\mathrm{2}\right)\:{x}^{\mathrm{2}} −\mathrm{3}{x}−{a}+\mathrm{2}=\mathrm{0} \\ $$$$\left(\mathrm{1}\right)\:−\:\left(\mathrm{2}\right) \\ $$$$\mathrm{4}{x}−\mathrm{2}=\mathrm{0}\:\Rightarrow\:{x}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\Rightarrow\:{a}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$
Commented by Rasheed.Sindhi last updated on 19/Dec/21
$$\cap\mathrm{i}\subset\in!\:\:\:\mathbb{T}\mathrm{han}\Bbbk\mathrm{s}\:\boldsymbol{\mathrm{sir}}. \\ $$