2019 CIME I Problems/Problem 13

Suppose $\text{P}$ is a monic polynomial whose roots $a$, $b$, and $c$ are real numbers, at least two of which are positive, that satisfy the relation \[a(a-b)=b(b-c)=c(c-a)=1.\] Find the greatest integer less than or equal to $100|P(\sqrt{3})|$.

Solution

Don't ask how, but it's 981.

See also

2019 CIME I (ProblemsAnswer KeyResources)
Preceded by
Problem 12
Followed by
Problem 14
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All CIME Problems and Solutions

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