Our olympic course professor gave us some exercises, and among these there is one which resolution is particularly instructive. Find the sum of the fifth powers of the roots of: To solve it, we need to write the recursion which is associated to the polynomial, which is: This recursion will give us the sum of […]

# Category: Polynomials

## Algebra Problem From Yesterday’s Simulation

Given two polynomials and , let a, b, c, d be the roots of , find First, notice that We know that plugging a, b, c, or d into gives 0, so we have to find the sum of squares of the roots minus the sum of the roots plus 4. By Vieta’s Theorem, the […]

## Old But Gold Polynomials

This article is about a couple of problems about polynomials which I regard as highly instructive. Seems A Demon But It’s Really Not I first saw this problem in 2018, and I initially thought it was a very hard problem, except it wasn’t. But, at first sight, it could make you feel a bit lost. […]