Sums and polynomials?
Given
is the root of a monic third degree polynomial with integral coefficients. Find the sum of coefficients of the polynomial.
This problem would not be possible if not for the awesome problem The Hydra . A good tip would be to try out that problem first.
This problem is part of the set ... and polynomials
The answer is 2.
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1 solution
A detailed solution will take long, but here's a brief guide:
Situation: given 1, in each operation you can -1, or +3 with equal probability. What is the chance that after finite number of steps, it will result in 0?
This is the Hydra problem. In the top solution two methods are given. By equating the two we get the answer.