Let a = {x | X & sup2; + 4x = 0}, B {X & sup2; + 2 (a + 1) x + A & sup2; - 1 = 0, a ∈ r}, if B is a subset of a, find the real number a

Let a = {x | X & sup2; + 4x = 0}, B {X & sup2; + 2 (a + 1) x + A & sup2; - 1 = 0, a ∈ r}, if B is a subset of a, find the real number a

A=｛X|X²＋4X=0｝={0,-4}
B is a subset of a, which is empty in four cases, {0}, {- 4}, {0, - 4}
Empty, 4 (a + 1) ^ 2-4 (A & sup2; - 1) < 0 → 8A + 8 < 0, a < - 1
{0}, a + 1 = 0 and a & sup2; - 1 = 0 → a = - 1
{- 4}, 2 (a + 1) = 8 and a & sup2; - 1 = 16, no solution
{0, - 4}, 2 (a + 1) = 4 and a & sup2; - 1 = 0 → a = 1
A ≤ - 1 or a = 1

The known function g (x) = ax square - 2aX + 1 + B (a ≠ 0, b)

1. G (x) = a (x-1) ^ 2 + 1-A + B, axis of symmetry x = 1,
So the function is monotone in [2,3],
(1) When a > 0, the opening of the parabola is upward, and the function is an increasing function in [2,3], so
1 = a (2-1) ^ 2 + 1-A + B, and 4 = a (3-1) ^ 2 + 1-A + B,
The solution is a = 1, B = 0;
(2) When a

A derivative problem: given the function f (x) = (AX ^ 2-2ax + 3a-2) e ^ x (a ≥ 0), its domain of definition is [0, + ∞) (1) find the monotone interval of F (x)
(2) If the minimum value of F (x) in [0, + ∞) is 4, find the value of A
I'm very grateful to you for helping me. The main question is the second one

F '(x) = (AX ^ 2 + A-2) e ^ x (1) if a ≥ 2, then f' (x) ≥ 0 for any x ∈ [0, + ∞), and f '(x) increases monotonically on [0, + ∞). ② if a = 0, then f' (x) < 0 for any x ∈ [0, + ∞), and f '(x) decreases monotonically on [0, + ∞). ③ if 0 < a < 2, from F' (x) = 0, x = (- 1 + 2 / a