The quadratic formula

give the roots of a quadratic equation which may be real or imaginary. The ± sign in the radical indicates that

and

where x_{1} and x_{2} are the roots of the quadratic equation ax^{2} + bx + c = 0. The sum of roots x_{1} + x_{2} and the product of roots x_{1}·x_{2} are common to problems involving quadratic equation.

**Derivation of the Sum of Roots**

**Derivation of the Product of Roots**

By difference of two squares:

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