Evaluating Expressions Given in Terms of Roots of Quadratic Equations
If a quadratic equation
has roots
and
then we can write the equation as
Expanding the brackets gives
(1)
Suppose that we have the equation
with rootsandthen comparing with (1) gives
and 
We can use simple algebra to evaluate many expressions given in terms ofand
without ever knowing what the values ofand
Example:
Example:
Example:
Example:
Example:
Any function symmetric in terms ofandcan be evaluated in this way. Symmetric here means that ifandare interchanged then the expression is unchanged:
This is the third example above.