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2025 SSMO Team Round Problems/Problem 4

Revision as of 11:31, 9 September 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>P(x) = x^2 - ax + b</math> be a quadratic with nonzero real coefficients. Given that <math>P(a)</math> and <math>P(-b)</math> are roots of <math>P(x),</...")
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Problem

Let $P(x) = x^2 - ax + b$ be a quadratic with nonzero real coefficients. Given that $P(a)$ and $P(-b)$ are roots of $P(x),$ there exists a value of $c$ such that $P(c)$ is constant for all possible $P(x)$. Find $c$.

Solution

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