PolynomialAndEquation FunctionEquation AMC10/12
2011


Problem - 613
Let $f(x)=ax^2+bx+c$, where $a$, $b$, and $c$ are integers. Suppose that $f(1)=0$, $50 < f(7) < 60$, $70 < f(8) < 80$, $5000k < f(100) < 5000(k+1)$ for some integer $k$. What is $k$?

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