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The quadratic $$ax^2 + bx + a = 0$$ has a positive coincident root $$\alpha$$. Then $$\alpha =$$ _________.
Correct Answer: 1
The product of the roots is $$\frac{a}{a} = 1$$, and with coincident roots this is $$\alpha^2 = 1$$. Since $$\alpha > 0$$, $$\alpha = 1$$ (this happens when $$b = -2a$$).
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