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Omni-MATH / Let f(x)=cx(x−1), where c is a positive real number. We use f^(n)(x) to denote the polynomial obtained by composing f with itself n times. For every positive integer n, all the roo…

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problem

Let f(x)=cx(x−1)f(x)=c x(x-1), where cc is a positive real number. We use fn(x)f^{n}(x) to denote the polynomial obtained by composing ff with itself nn times. For every positive integer nn, all the roots of fn(x)f^{n}(x) are real. What is the smallest possible value of cc?
Plain-text mathematical notation (without MathML)
Let f(x)=cx(x−1), where c is a positive real number. We use f^(n)(x) to denote the polynomial obtained by composing f with itself n times. For every positive integer n, all the roots of f^(n)(x) are real. What is the smallest possible value of c?
Original LaTeX notation
Let $f(x)=c x(x-1)$, where $c$ is a positive real number. We use $f^{n}(x)$ to denote the polynomial obtained by composing $f$ with itself $n$ times. For every positive integer $n$, all the roots of $f^{n}(x)$ are real. What is the smallest possible value of $c$?

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task_id
8fb5ca99-a137-5885-bfa6-d0d17c106021
task_key
test--8fb5ca99-a137-5885-bfa6-d0d17c106021
task_revision_id
1
config / split
/ test

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