F'(x) = 3ax^2 + 12x + b .............(1) Applying the formula for solving any quadratic leads to two equations: (-12 + sq rt(144 - 12ab))/6a = 2 .................(2) (-12 - sq rt(144 - 12ab))/6a = -1 .................(3) Adding equations (2) and (3) , we get: -24/6a = 1 a = -4 Plugging the value a = -4 into equation (2) and solving for b, we get: b = 24.