Roots of Quadratic Equations: Summary
Roots of Quadratic Equations: Summary
First recall the quadratic formula
The expression 
that appears under the square root sign determines the nature of the roots. It is called the discriminant of the equation.
, the equation has only one root 
, called double root. It is not hard to prove that in this case, we have
, the equation has two distinct real roots 
and 
. In this case, we have
If you try to prove the above equation, make use of the following identities:
As a matter of fact, if two numbers and satisfy the above identities, then they are solutions to the quadratic equation 
.
, the equation has two distinct complex roots that are conjugates of each other
