Discriminant
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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.
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
.