Quadratic equations
A quadratic equation is an equation of the form: ax² + bx + c=0.
From secondary school mathematics we know that all quadratic equations can be solved using the formula:

This formula includes the "plus or minus" sign ±, which means that the formula can produce two different values for x. The following example shows a typical example of using the formula where the equation has two solutions.

The formula will work whether or not the quadratic equation can be factorised. When b²-4ac > 0 there are two different real solutions, when b²-4ac=0 there are two identical real solutions.

The case when b²-4ac < 0 is ignored at main school level - or else you are told there are "no solutions" - but those studying mathematics to a higher level will know that in this case there are still two solutions, but they are complex numbers.

If you have installed the plugin (see Tech), find out more about solutions to quadratic equations.