2014 AMC 12B Problems/Problem 16
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Problem
Let be a cubic polynomial with , , and . What is ?
$\textbf{(A)}\ 0\qquad\textbf{(B)}\ k\qquad\textbf{(C)}\ 6k\qquad\textbf{(D)}}\ 7k\qquad\textbf{(E)}\ 14k$ (Error compiling LaTeX. Unknown error_msg)
Solution
Let . Plugging in for , we find , and plugging in and for , we obtain the following equations: Adding these two equations together, we get If we plug in and in for , we find that Multiplying the third equation by and adding gives us our desired result, so