Maths Olympiad Prep

Track / Stage 5 / 225 of 400 #825 of 1964

Problem 825

AIME late
Algebra Difficulty 5.4 Find the answer

In a quadratic trinomial, the first coefficient and the constant term were swapped, after which the result was added to the original trinomial. This resulted in a third quadratic trinomial, which turned out to have a single root. What can this root be equal to? If there are multiple correct answers, list them separated by commas or semicolons.

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

Answer: 1,11,11;11;1-1,1|1,-1| 1 ;-1 |-1 ; 1

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.