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2020 PUMaC Algebra A4 / B6

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January 1, 2022
algebra

Problem Statement

Let PP be a 1010-degree monic polynomial with roots r1,r2,...,r10≠r_1, r_2, . . . , r_{10} \ne and let QQ be a 4545-degree monic polynomial with roots 1ri+1rj−1rirj\frac{1}{r_i}+\frac{1}{r_j}-\frac{1}{r_ir_j} where i<ji < j and i,j∈{1,...,10}i, j \in \{1, ... , 10\}. If P(0)=Q(1)=2P(0) = Q(1) = 2, then log⁡2(∣P(1)∣)\log_2 (|P(1)|) can be written as a/ba/b for relatively prime integers a,ba, b. Find a+ba + b.
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