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Difference between revisions of "2021 Fall AMC 10A Problems/Problem 25"

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== Problem ==
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#REDIRECT [[2021_Fall_AMC_12A_Problems/Problem_23]]
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A quadratic polynomial with real coefficients and leading coefficient <math>1</math> is called <math>\emph{disrespectful}</math> if the equation <math>p(p(x))=0</math> is satisfied by exactly three real numbers. Among all the disrespectful quadratic polynomials, there is a unique such polynomial <math>\tilde{p}(x)</math> for which the sum of the roots is maximized. What is <math>\tilde{p}(1)</math>?
 
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<math>\textbf{(A) } \frac{5}{16} \qquad\textbf{(B) } \frac{1}{2} \qquad\textbf{(C) } \frac{5}{8} \qquad\textbf{(D) } 1 \qquad\textbf{(E) } \frac{9}{8}</math>
 

Latest revision as of 23:07, 23 November 2021

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