Solving Quadratic Equations

A quadratic equation is an equation that can be written in the form \(ax^2+bx+c=0\) where \(a,b,c\in \mathbb{R}\); i.e. where \(a,b,c \) are real numbers. In short, a quadratic equation is an equation involving polynomials of degree no greater than \(2\).

In the lessons that follow, we will discuss several different methods for solving quadratic equations, including a “blanket” method that will solve any quadratic equation no matter what.

As usual, “solving an equation” usually means finding \(x\)-values that make an equation true. When it comes to quadratic equations, there will never be more than \(2\) unique solutions to an equation.