Mathematics » Equations and Inequalities » Solving Quadratic Equations

A quadratic equation is an equation where the exponent of the variable is at most $$\text{2}$$. The following are examples of quadratic equations:

\begin{align*} 2{x}^{2} + 2x & = 1 \\ 3{x}^{2} + 2x – 1 & = 0 \\ 0 & = -2{x}^{2} + 4x – 2 \end{align*}

Quadratic equations differ from linear equations in that a linear equation has only one solution, while a quadratic equation has at most two solutions. There are some special situations, however, in which a quadratic equation has either one solution or no solutions.

We solve quadratic equations using factorisation. For example, in order to solve $$2{x}^{2} -x – 3 = 0$$, we need to write it in its equivalent factorised form as $$(x + 1)(2x – 3) = 0$$. Note that if $$a \times b = 0$$ then $$a = 0$$ or $$b = 0$$.

The following video shows an example of solving a quadratic equation by factorisation.