Question Number 12305 by Gaurav3651 last updated on 18/Apr/17
$${If}\:{c}>\mathrm{0}\:{and}\:\mathrm{4}{a}+{c}<\mathrm{2}{b},{then} \\ $$ $${ax}^{\mathrm{2}} −{bx}+{c}=\mathrm{0}\:{has}\:{a}\:{root}\:{in}\:{which} \\ $$ $${intervals}? \\ $$ $$\left({a}\right)\:\:\left(\mathrm{0},\mathrm{2}\right) \\ $$ $$\left({b}\right)\:\:\left(\mathrm{2},\mathrm{3}\right) \\ $$ $$\left({c}\right)\:\:\left(\mathrm{3},\mathrm{4}\right) \\ $$ $$\left({d}\right)\:\:\left(−\mathrm{2},\mathrm{0}\right) \\ $$
Answered by ajfour last updated on 18/Apr/17
$${f}\left(\mathrm{0}\right)={c}\:>\mathrm{0}\:\:;\:\:{f}\left(\mathrm{2}\right)=\:\mathrm{4}{a}−\mathrm{2}{b}+{c}\:<\mathrm{0} \\ $$ $${so}\:{f}\left({x}\right)=\:{ax}^{\mathrm{2}} −{bx}+{c}\: \\ $$ $${has}\:{a}\:{root}\:{in}\:\left(\mathrm{0},\mathrm{2}\right)\:. \\ $$