A polynomial equation in which the highest power of x is 2, is called a quadratic equation. There are 3 methods that can be used to solve quadratic equations:

1. Factorising.
2. Completing the square.
3. The Quadratic Formula.

You should be familiar with methods 1 and 3 from G.C.S.E., but you may not have looked at the second method.

The Quadratic Formula also offers a quick way to check whether a quadratic equation has solutions. To skip to this click here.

Quadratic expressions can often be factorised into 2 brackets. When this can be done it offers an easy way to solve a quadratic equation. For example, consider the equation 

This can be factorised, to give

You should already be familiar with this method, so we will only look at one more example. 

Solve the equation

When you have a number in front of the x² term, the only way to factorise is by trial and error. We know that in the brackets the co-efficients of x must multiply to give 4 and the numbers must multiply to give 21.

Try different combinations until you find one that expands to give 20x.

 The equation is therefore

Therefore the solutions are

Not all quadratic expressions can be factorised. In these cases the equation can be solved by completing the square.

[footer.htm]