If a is positive  and the discriminant of ax2 + 2bx + c is negative, then abax+bbcbx+cax+bbx+c0 is

Here a > 0 and 4b2 - 4ac < 0, i.e., ac - b2 > 0.∴ ax2+2bx+c>0,∀x∈RNow,abax+bbcbx+c00−ax2+2bx+c          [Operating R3→R3−xR1−R2   =−ax2+2bx+cac−b2   =−(+ve)(+ve)=−ve