If the solution set of inequality ax & # 178; + BX + C ＞ 0 (a ≠ 0) is an empty set, then the condition that coefficients a, B, C should satisfy is

If the solution set of inequality ax & # 178; + BX + C ＞ 0 (a ≠ 0) is an empty set, then the condition that coefficients a, B, C should satisfy is

That is, the image opening of the quadratic function y = ax & # 178; + BX + C is downward, and there is an intersection or no intersection with the X axis
So a

The solution set of inequality ax & # 178; - BX + C > 0 is (- 1 / 2,2). For the coefficients a, B, C, we have the following conclusions: 1, a > O, 2, b > 0, 3C > 0

From the inequality ax & # 178; - BX + C > 0, the solution set is (- 1 / 2,2)
Know a 0
It can be reduced to a (x + 1 / 2) (X-2) > 0 (a)

If the solution set of inequality ax + BX + 2 > 0 is {x | - 1 / 2

-1/2+1/3=-1/6=-b/a
a=6b
(-1/2)(1/3)=-1/6=2/a
a=-12
b=-2
a+b=-14

It is known that the quadratic function y = ax ^ 2 + BX + C, and the solution of inequality ax ^ 2 + BX + C ＞ - 2x is 1 < x < 3,
1. If the equation AX ^ 2 + BX + C + 6A = 0 has two equal roots, find the analytic expression of the function
2. If the maximum value of the function is a positive number, find the range of A

Let f (x) = ax ^ 2 + BX + C, then f (x) > - 2x, that is, the solution of ax ^ 2 + (B + 2) x + C > 0 is (1,3),
A0, and from (1) (2) (3) above
-2-√3