If \alpha and \beta are the roots of the quadratic equation x^2+\alpha x+\beta=0, where \beta \neq 0, then what is the value of \alpha-\beta?

Explanation

Using sum and product of roots: \alpha + \beta = -\alpha \implies 2\alpha + \beta = 0, and \alpha\beta = \beta. Since \beta \neq 0, \alpha = 1. Substituting \alpha=1 into the sum yields \beta = -2. The difference is \alpha - \beta = 1 - (-2) = 3.

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