Quadratic Equations Problems

A quadratic equation is a polynomial equation of degree two, typically written in the form ax² + bx + c = 0 where a ≠ 0. These equations can be solved using various methods including factoring, completing the square, and the quadratic formula. The solutions, called roots, can be real or complex numbers and represent the x-intercepts of the corresponding parabola. Quadratic equations model numerous real-world phenomena including projectile motion, area optimization, and profit maximization. Understanding the discriminant (b² - 4ac) helps determine the nature and number of solutions. This topic is fundamental to algebra and serves as a gateway to higher-degree polynomial equations.