If A and B are the roots of the equation Ax² - A²x + AB = 0, then what are the values of A and B, respectively?

Using Vieta's formulas on the equation Ax^2 - A^2x + AB = 0, the sum of the roots is A + B = A^2 / A, which simplifies to A + B = A, meaning B must be 0. The product of the roots is A * B = AB / A, which simplifies to AB = AB, providing no new information. Since the first root is named A, we can substitute B = 0 into the original equation for the second root, but to satisfy the sum equation A + B = A, if A is 1, then B is 0. Therefore, the respective values of A and B are 1 and 0.

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