This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 27

2012 Tuymaada Olympiad, 2
Let $P(x)$ be a real quadratic trinomial, so that for all $x\in \mathbb{R}$ the inequality $P(x^3+x)\geq P(x^2+1)$ holds. Find the sum of the roots of $P(x)$. [i]Proposed by A. Golovanov, M. Ivanov, K. Kokhas[/i]
inequalities sum of roots polynomial quadratic algebra polynomials quadratic equations

2020 BMT Fall, 2
Let $a$ and $b$ be the roots of the polynomial $x^2+2020x+c$. Given that $\frac{a}{b}+\frac{b}{a}=98$, compute $\sqrt c$.
sum of roots polynomial algebra polynomials