Students learn the sum and product of roots formula, which states that if the roots of a quadratic equation are given, the quadratic equation can be written as 0 = x^2 - (sum of roots)x + (product of roots). For example, to write a quadratic equation that has the given roots -9 and 4, the first step is to find the sum and product of the roots. Since the sum of the roots is -5, and the product of the roots is -36, the quadratic equation can be written as 0 = x^2 - (-5)x + (-36), which simplifies to 0 = x^2 + 5x - 36.

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