Quadratic Equations

A quadratic equation is formed when

A quadratic equation is formed when a quadratic polynomial (degree 2) is equated to zero. Standard form: ax² + bx + c = 0, where a ≠ 0, and a, b, c ar

Step

Step-by-step process: 1) Write equation in standard form, 2) Factor the quadratic expression into two linear factors, 3) Set each factor equal to zero

Universal formula

Universal formula: x = (-b ± √(b² - 4ac))/2a. Derivation involves completing the square method. Steps: 1) Identify a, b, c from standard form, 2) Calc

Discriminant D = b²

Discriminant D = b² - 4ac determines root types: D > 0 gives two distinct real roots, D = 0 gives two equal real roots (coincident), D < 0 gives no re

Common problem types

Common problem types: 1) Consecutive numbers: If first is x, next odd/even is x+2, 2) Area problems: length × width = area, 3) Age problems: present a