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ASU 359 All Soviet Union MO 1983 training in square equation solution

Source:

July 28, 2019
combinatoricsgame strategymaximum

Problem Statement

The pupil is training in the square equation solution. Having the recurrent equation solved, he stops, if it doesn't have two roots, or solves the next equation, with the free coefficient equal to the greatest root, the coefficient at xx equal to the least root, and the coefficient at x2x^2 equal to 11. Prove that the process cannot be infinite. What maximal number of the equations he will have to solve?
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