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The roots of the equation 2x^2 - 5x - 4 = 0 can be written in the form x = (m±sqrt n)/p, where m, n, and p are positive integers with a greatest common divisor of 1. What is the value of n?

 

Thanks :D

AnonymousConfusedGuy  Jan 16, 2018
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2+0 Answers

 #1
avatar+85862 
+1

2x^2 -5x  - 4  = 0     divide through by 2

 

x^2  - 5/2 x  -  2   =  0      add 2 to both sides

 

x^2  -  5/2 x   =  2        take 1/2 of 5/2  = 5/4.....square it =  25/16...add to both sides

 

x^2  -5/2 x  +  25/16   =  2 +  25/16      simplify both sides

 

(x  - 5/4)^2  =  57/16     take both rots

 

x - 5/4   = ±√57 / 4       add  5/4 to both sides

 

x  =  [  ±√57   +  5  ]  / 4

 

So...n  = 57

 

 

cool cool cool

CPhill  Jan 16, 2018
 #2
avatar+941 
+1

Thank you! :D

AnonymousConfusedGuy  Jan 16, 2018

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