Difference between revisions of "2024 AMC 8 Problems/Problem 10"

(Solution 1)
(Problem)
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==Problem==
 
==Problem==
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What is the sum of the roots of <math>\frac{1}{x}</math> <math>+1=x</math>?
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A)0  B)-1  C)1  D)-2  E)2
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==Solution 1==
 
==Solution 1==
 
(joke problem but decided to answer it)The answer is C. If you multiply the equation by x you get 1+x=x^2 . Now moving it to a quadratic you get -x^2+x+1 . Using Vieta's -b/a is -1/-1 which is 1.
 
(joke problem but decided to answer it)The answer is C. If you multiply the equation by x you get 1+x=x^2 . Now moving it to a quadratic you get -x^2+x+1 . Using Vieta's -b/a is -1/-1 which is 1.
  
 
-Multpi12
 
-Multpi12

Revision as of 11:30, 21 January 2024

Problem

What is the sum of the roots of $\frac{1}{x}$ $+1=x$?

A)0 B)-1 C)1 D)-2 E)2

Solution 1

(joke problem but decided to answer it)The answer is C. If you multiply the equation by x you get 1+x=x^2 . Now moving it to a quadratic you get -x^2+x+1 . Using Vieta's -b/a is -1/-1 which is 1.

-Multpi12