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HMMT 二月 2010 · CALC 赛 · 第 1 题

HMMT February 2010 — CALC Round — Problem 1

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 3 ] Suppose that p ( x ) is a polynomial and that p ( x ) − p ( x ) = x + 2 x + 1. Compute p (5).
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解析

英文解析

  1. [ 3 ] Suppose that p ( x ) is a polynomial and that p ( x ) − p ( x ) = x + 2 x + 1. Compute p (5).
    Answer: 50 Observe that p ( x ) must be quadratic. Let p ( x ) = ax + bx + c . Comparing coefficients 2
    gives a = 1, b − 2 a = 2, and c − b = 1. So b = 4, c = 5, p ( x ) = x + 4 x + 5 and p (5) = 25 + 20 + 5 = 50.2
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