Discriminant
From AoPSWiki
The discriminant of a quadratic equation of the form 
is the quantity 
. When 
are real, this is a notable quantity, because if the discriminant is positive, the equation has two real roots; if the discriminant is negative, the equation has two nonreal roots; and if the discriminant is 0, the equation has a real double root.
Contents |
Example Problems
Introductory
- (AMC 12 2005) There are two values of
for which the equation 
has only one solution for 
. What is the sum of these values of ?
Solution: Since we want the 's where there is only one solution for , the discriminant has to be 
. 
. The sum of these values of is 
.
