Problem:
There are two values of for which the equation has only one solution for . What is the sum of those values of
Answer Choices:
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B.
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E.
Solution:
The quadratic formula yields
The equation has only one solution precisely when the value of the discriminant, , is 0 . This implies that or , and the sum is -16 .
OR
The equation has one solution if and only if the polynomial is the square of a binomial with linear term and constant term . Because has a linear term , it follows that . Thus is either -20 or 4 , and the sum of those values is .
The problems on this page are the property of the MAA's American Mathematics Competitions