Given the set a = {x | AX3 + ax2-x = 0}, if the set a is a single element set, then the value range of real number a is______ ． | Math enthusiast | Mathematical art

Given the set a = {x | AX3 + ax2-x = 0}, if the set a is a single element set, then the value range of real number a is______ ．

Let AX3 + ax2-x = x (AX2 + AX-1) = 0, then x = 0, or AX2 + AX-1 = 0, from the set a is a single element set, so the equation AX2 + AX-1 = 0 has no real number solution. When a = 0, the condition is satisfied. When a ≠ 0, △ = A2 + 4A < 0, the solution is: - 4 < a < 0. In conclusion, the value range of real number a is (- 4,0], so the answer is: (- 4,0]

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