What is the Formula for Sum of Roots?

The formula for the sum of the roots of a quadratic equation is derived from the coefficients of the equation.

Sum of Roots of a Quadratic Equation

For a general quadratic equation in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0, the sum of the roots (α + β) is given by:

α + β = -b/a

This formula provides a quick way to find the sum of the roots without actually solving for the roots themselves.

Explanation

• a: Coefficient of the x² term.
• b: Coefficient of the x term.
• c: Constant term.
• α and β: The roots of the quadratic equation.

Example

Consider the quadratic equation 2x² + 5x + 3 = 0.

• Here, a = 2 and b = 5.
• Using the formula, the sum of the roots is -b/ a = -5/2.

Table Summarizing Formulas for Quadratic Equations

Property	Formula
Sum of Roots	-b/a
Product of Roots	c/a

According to the reference, for a quadratic equation ax² + bx + c = 0, the sum of the roots (α + β) is equal to -b/ a.