Quadratic Equation - GCSE Maths Definition

A quadratic equation is an equation that is written in, or can be rearranged to, the form

ax² + bx + c = 0

where a, b and c are constants and x is the unknown variable.
A quadratic equation must have a term involving x2, and this will be the highest power of x that appears in the equation.
i.e. a ≠ 0 (this would make it a linear equation); it is possible that b and/or c equal zero, and these would lead to special cases of quadratic equations.

Quadratic equations will either have no (real) solutions, 1 (real) solution - sometimes called a repeated solution - or 2 (real) solutions. Quadratic equations can be solved by factorising, completing the square or by using the quadratic formula.

In GCSE Mathematics, you may be asked to solve a quadratic equation in a particular way, or it may be left up to you. You may have a calculator that can solve quadratic equations for you (but remember to show sufficient working to get method marks!). Interpreting the solution(s) to a quadratic equation may also be required; for example, x could be the time, or times, at which a thrown ball is at a certain height above ground level.