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December 12th, 2007, 07:47 PM  #1 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  Second Degree Polynomials
Student A and B were taking an math test in high school. They were solving for ax^2 + bx + c = 0. But, student A misread the coefficient a, and he arrived with the answer x = 1 + sqrt(6) and x = 1  sqrt(6). The student B misread the coeffieicnt c, and he arrived with the answer x = 1/3 and x = 1. Using the information above, determine the actual roots (x = ...?) for ax^2 + bx + c = 0. 
December 12th, 2007, 09:20 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,975 Thanks: 2225 
Since student A thought the equation was a multiple of xÂ² âˆ’ 2x âˆ’ 5 = 0 and student B thought the equation was a multiple of 3xÂ² âˆ’ 2x âˆ’ 1 = 0, the equation must have been a multiple of 3xÂ² âˆ’ 2x âˆ’ 5 = 0, which has solutions x = âˆ’1 or 5/3.


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