Quadratic Equations

A quadratic equation in variable x

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

A real number α is called

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). In other wor

If a quadratic equation ax² +

If a quadratic equation ax² + bx + c = 0 can be factored into two linear factors, say (px + q)(rx + s) = 0, then the roots can be found by setting eac

This method transforms the quadratic equation

This method transforms the quadratic equation into a perfect square form (x - p)² = q. The process involves: (1) Rearrange to ax² + bx = -c, (2) Divid

For any quadratic equation ax² +

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