2021 JMPSC Invitationals Problems/Problem 1
The equation where is some constant, has as a solution. What is the other solution?
Since must be a solution, must be true. Therefore, . We plug this back into the original quadratic to get . We can solve this quadratic to get . We are asked to find the 2nd solution so our answer is
Plug to get , so , or , meaning the other solution is ~Geometry285
Plugging in , we get , therefore, Finally, we get the other root is .
- kante314 -
We can rearrange the equation to get that . Then, by Vieta's Formulas, we have and where is the second root of the quadratic. Solving for tells us that the answer is .
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