The general solution of the quadratic equation
is
and
If
then
and
are distinct real numbers.and can be plotted on the
- axis, abd the graph
will pass though the points
and
If
then
and the graphjust touches the– axis but does not cross it. If
the m to find x-1 and x-2 we must take the square root of a negative number.andare not real numbers and cannot be plotted on the – axis. The graph does not cross the– axis, butandare still solutions to
The square root of a negative number is said to be 'complex' and labelled with the letter
:
and
Complex numbers have many uses, in geometry, electricity, quantum mechanics, trigonometry, number theory...
Example: If
then
and
