Mathematics » Equations and Inequalities » Solving Quadratic Equations

Solving Quadratic Equations

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.

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