Quadratic inequalities are solved in very much the same way as quadratic equations – first setting one side to 0 and finding the roots. It is very important to remember here that quadratic equations have equality – where you are looking for roots i.e. where the quadratic cuts the x-axis. When solving quadratic inequalities you are not looking for roots, you are looking to see where the graph is positive or negative. Finding the roots is helpful as it tells you where the graph changes from being positive to negative or vice versa.
can be factorised to
. The roots would be x=3 and x=-2 meaning that the graph is positive if we choose any x more than 3 or x less than -2. The solution is