Mock AIME 3 Pre 2005 Problems/Problem 3
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Problem
A function is defined for all real numbers . For all non-zero values , we have
Let denote the sum of all of the values of for which . Compute the integer nearest to .
Solution
Substituting , we have
This gives us two equations, which we can eliminate from (the first equation multiplied by two, subtracting the second):
Clearly, the discriminant of the quadratic equation , so both roots are real. By Vieta's formulas, the sum of the roots is the coefficient of the term, so our answer is .
See Also
Mock AIME 3 Pre 2005 (Problems, Source) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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