Question Number 178715 by CrispyXYZ last updated on 20/Oct/22
![The solution of 2≤ax^2 +bx+c≤3 is [2, 3] 1) if a>0, ax^2 +(b−3)x−c≤0 has and only has 10 integer solutions. find the range of a. 2) find x: ax^2 +(b−1)x+5<0](Q178715.png)
$$\mathrm{The}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{2}\leqslant{ax}^{\mathrm{2}} +{bx}+{c}\leqslant\mathrm{3}\:\mathrm{is}\:\left[\mathrm{2},\:\mathrm{3}\right] \\ $$ $$\left.\mathrm{1}\right)\:\mathrm{if}\:{a}>\mathrm{0},\:{ax}^{\mathrm{2}} +\left({b}−\mathrm{3}\right){x}−{c}\leqslant\mathrm{0}\:\mathrm{has}\:\mathrm{and}\:\mathrm{only}\:\mathrm{has}\:\mathrm{10}\:\mathrm{integer}\:\mathrm{solutions}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{a}. \\ $$ $$\left.\mathrm{2}\right)\:\mathrm{find}\:{x}:\:{ax}^{\mathrm{2}} +\left({b}−\mathrm{1}\right){x}+\mathrm{5}<\mathrm{0} \\ $$