2014 AIME II Problems/Problem 5
Problem 5
Real numbers and are roots of , and and are roots of . Find the sum of all possible values of .
Solution
Let , , , and be the roots of (per Vieta's). Then and similarly for . Also,
Set up a similar equation for :
Simplifying and adding the equations gives
Now, let's deal with the . Equating the a in both equations (per Vieta) which eventually simplifies to
Substitution into (*) should give and , corresponding to and , and , for an answer of .
See also
2014 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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