Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 5.1 AIME, harder Prove it Philippines

Problem:
Find the values of $a$ and $b$ such that $a x^{4} + b x^{2} + 1$ is divisible by $x^{2} - x - 2$ .

Solution

Solution:
$a = \frac{1}{4},\ b = -\frac{5}{4}$

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.