# Difference between revisions of "1984 AIME Problems/Problem 12"

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== Problem == | == Problem == | ||

+ | A function <math>\displaystyle f</math> is defined for all real numbers and satisfies <math>\displaystyle f(2+x)=f(2-x)</math> and <math>\displaystyle f(7+x)=f(7-x)</math> for all <math>\displaystyle x</math>. If <math>\displaystyle x=0</math> is a root for <math>\displaystyle f(x)=0</math>, what is the least number of roots <math>\displaystyle f(x)=0</math> must have in the interval <math>\displaystyle -1000\leq x \leq 1000</math>? | ||

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== Solution == | == Solution == | ||

{{solution}} | {{solution}} |

## Revision as of 01:30, 21 January 2007

## Problem

A function is defined for all real numbers and satisfies and for all . If is a root for , what is the least number of roots must have in the interval ?

## Solution

*This problem needs a solution. If you have a solution for it, please help us out by adding it.*