For how many quadratic equations, the sum of roots is equal to the product of roots?

Explanation

For a quadratic equation ax^2 + bx + c = 0, the sum of roots is -b/a and the product is c/a. Setting them equal gives -b/a = c/a, which implies b = -c. Since there are infinitely many combinations of a, b, and c that satisfy this condition (e.g., a=1, b=-2, c=2), there are infinitely many such equations.

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