# Quadratic functions - Discriminant and Roots

This applet investigates the discriminant of a quadratic function, and how its affects the number and values of the roots (solutions) of a quadratic equation. There is an option to see the complex number roots when the discriminant is negative.

###### Author and programmer: Ron Barrow

UK Years 12-13, KS5, KS4, Core 1 (C1) GCE Mathematics, Algebra and Functions
also: Further Mathematics (OCR, Edexcel) FP1
US - Grades 11 - 12

Instructions below    See also:    Quadratics: Completing the Square    Quadratic Inverses   Quadratic Inequalities
Complex numbers 1    blog post

## How to Use this Applet

The applet on this page is designed to help you understand how to the disciminant helps you when dealing with quadratic equations and expressions.
The general quadratic expression is: ax² + bx + c.
The discriminant is: b² - 4ac. Varying a, b, c changes the curve. You can do this by clicking in the three boxes at the bottom and dragging left or right. As the curve changes, notice how the discriminant changes. It's a good to idea to make things a little easier to begin by keeping a = 1. The discriminant helps you in deciding whether or not a quadratic equation has 2, 1 or no real solution, as well as going half-way to finding the roots (solutions) of the equation, as quadratic formula includes the discriminant.
Further Mathematics: If you check the box "Complex roots", you can see the conjugate pair of complex roots when the discriminant is negative. Enjoy.