Given the function f (x) = (x2-x-1 / a) e ^ ax (a > 0), if the inequality f (x) + 3 / a > = 0 holds for X ∈ (- 3 / A, + infinity), then the value range of real number a is?

Given the function f (x) = (x2-x-1 / a) e ^ ax (a > 0), if the inequality f (x) + 3 / a > = 0 holds for X ∈ (- 3 / A, + infinity), then the value range of real number a is?

Given the function f (x) = (x2-x-1 / a) e ^ ax (a > 0), if the inequality f (x) + 3 / a > = 0 holds for X ∈ (- 3 / A, + infinity), then the value range of real number a is?
Analysis: ∵ function f (x) = (x ^ 2-x-1 / a) e ^ (AX) (a > 0), inequality f (x) + 3 / a > = 0 holds for X ∈ (- 3 / A, + infinity)
Let g (x) = f (x) + 3 / a = (x ^ 2-x-1 / a) e ^ (AX) + 3 / A
g’(x)=(ax^2+(2-a)x-2)e^(ax)=0==> ax^2+(2-a)x-2=0==>x1=1,x2=-2/a
g’’(x)=(a^2x^2+(4a-a^2)x+2-3a)e^(ax)
G '' (1) = a + 2 > 0, G (x) takes the minimum value at x1;
g’’(-2/a)=-(a+2)=0==>a0
The value range of a is 0