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Sum and Product of Roots

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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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