Question Number 5507 by Kasih last updated on 17/May/16
$${if}\:\left({x}−\mathrm{1}\right)\:\left({x}+\mathrm{1}\right)\:+\mathrm{3}{x}+{x}^{\mathrm{2}} ={ax}^{\mathrm{2}} +{bx}+{c}\:{then}\:{a}=?\:{b}=?\:{c}=? \\ $$
Answered by Rasheed Soomro last updated on 17/May/16
$$\:\left({x}−\mathrm{1}\right)\:\left({x}+\mathrm{1}\right)\:+\mathrm{3}{x}+{x}^{\mathrm{2}} ={ax}^{\mathrm{2}} +{bx}+{c} \\ $$$${x}^{\mathrm{2}} −\mathrm{1}+\mathrm{3}{x}+{x}^{\mathrm{2}} ={ax}^{\mathrm{2}} +{bx}+{c} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{1}={ax}^{\mathrm{2}} +{bx}+{c} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{x}+\left(−\mathrm{1}\right)={ax}^{\mathrm{2}} +{bx}+{c} \\ $$$${a}=\mathrm{2},{b}=\mathrm{3},{c}=−\mathrm{1} \\ $$