If the equation ax2+bx+c=0(a>0) has two roots α and β such that α<−2 and β>2, then

Let y = ax2 + bx + c consider the following cases :Case I D>0⇒b2−4ac>0Case II af(-2)<0→ a (4a -2b +c) <0 → 4a-2b +c<0Case III af(2)<0→ a(4a + 2b+ c)<0→ 4a+2b + c<0Combining Case lI and Case III, we get4a+2b+c<0Also, at x = 0, y <0⇒c<0Also, since for -2 < x <2,y <0ax2+bx +c <0For x= 1, a+b+ c <0 …..(i)and for x= -1, a -b+ c <0…..(ii)Combining Eqs. (i) and (ii), we geta+|b|+c<0