GlossariesGCSE GlossariesGCSE Maths GlossaryRoots

Roots - GCSE Maths Definition

Reviewed by: Dan Finlay

Published

In mathematics, the roots of a function are the values (or value, if only one) of the variable (input) that lead to the function (output) being zero.

There are a couple of ways to consider roots, which are related. Let's say we have the function f(x),

(i) the roots of the function are the solutions to the equation f(x) = 0,
(ii) the roots of the function are the values of x for which the graph of y = f(x) intersects the x-axis.

For example, the roots of the quadratic function

f open parentheses x close parentheses equals x squared space space minus 4

are the solutions to the equation

x squared minus 4 equals 0

which are

x equals 2 and x equals negative 2

  • The roots of the function f open parentheses x close parentheses equals x squared minus 4 are 2 and -2

  • The graph of y equals f open parentheses x close parentheses will intersect the x-axis at the points (-2, 0) and (2,0)

Roots and solutions are words that are used interchangeably in mathematics, with very slight differences depending on how what is being said is phrased.

Examiner-written GCSE Maths revision resources that improve your grades 2x

  • Written by expert teachers and examiners
  • Aligned to exam specifications
  • Everything you need to know, and nothing you don’t
GCSE Maths revision resources

Share this article

Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Subject Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

The examiner written revision resources that improve your grades 2x.

Join now