Quadratic Equations — Formula Sheet

A quadratic equation in variable x is of the form ax² + bx + c = 0, where a, b, c are real numbers and a ≠ 0.

The method is based on the Zero Product Property

if P × Q = 0, then P = 0 OR Q = 0.

To split the middle term

find two numbers p and q such that p + q = b and p × q = a × c.

This method converts ax² + bx + c = 0 into the form (x + k)² = d, which is easy to solve.

Formula

x = (-b ± √(b² - 4ac)) / 2a

A real number α is called a root of the quadratic equation ax² + bx + c = 0 if substituting x = α satisfies the equation (makes it true).

This method transforms the quadratic equation into a perfect square form (x - p)² = q.

For any quadratic equation ax² + bx + c = 0 where a ≠ 0, the roots are given by: x = [-b ± √(b² - 4ac)] / 2a.