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2001 AMC 12 Problems/Problem 19

Revision as of 23:05, 7 February 2009 by Duelist (talk | contribs) (New page: == Problem == The polynomial <math>p(x) = x^3+ax^2+bx+c</math> has the property that the average of its zeros, the product of its zeros, and the sum of its coefficients are all equal. The ...)
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Problem

The polynomial $p(x) = x^3+ax^2+bx+c$ has the property that the average of its zeros, the product of its zeros, and the sum of its coefficients are all equal. The $y$-intercept of the graph of $y=p(x)$ is 2. What is $b$?

$(\mathrm{A})\ -11 \qquad (\mathrm{B})\ -10 \qquad (\mathrm{C})\ -9 \qquad (\mathrm{D})\ 1 \qquad (\mathrm{E})\ 5$

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