User:DTR/Roots of a Quadratic

Introduction
A quadratic equation is any equation of the form $$ax^2 + bx + c = 0$$. All quadratics have two solutions, or roots. Remember from C1 that these roots may be equal, or not even real! We can also factorise a quadratic, to express it as two linear factors. This chapter is concerned with the roots of various quadratics, and the relationships between the roots.

So that we can refer to and manipulate the roots, we denote them with the Greek letters $$\alpha$$ and $$\beta$$, pronounced alpha and beta, respectively. It can be shown that the sum of the roots, $$\alpha + \beta = \frac{-b}{a} $$. Also, the product of the roots, $$\alpha \beta = \frac{c}{a}$$.