Sum and Product of Roots
The quadratic formula
give the roots of a quadratic equation which may be real or imaginary. The ± sign in the radical indicates that
where x1 and x2 are the roots of the quadratic equation ax2 + bx + c = 0. The sum of roots x1 + x2 and the product of roots x1·x2 are common to problems involving quadratic equation.
Derivation of the Sum of Roots
Derivation of the Product of Roots
By difference of two squares: