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avatar+2765 

Portia solved the quadratic equation \(x^2+(2\sqrt3)x+1=0\)  by completing the square. In the process, she came up with the equivalent equation \((x+r)^2 = s,\) where \(r\) \(s\) and  are constants.

What is \(s\)?

tertre  Mar 11, 2017

Best Answer 

 #2
avatar+87334 
+5

x^2 + 2sqrt(3)x + 1  = 0

 

x^2 + 2sqrt(3)x  = - 1         

 

Take (1/2) of 2sqrt(3)  = sqrt(3)....square this = 3   add to both sides

 

x^2 + 2sqrt(3)x + 3 =  -1 + 3      simpify and factor

 

(x  + sqrt(3) )^2   =    2

 

r =  sqrt(3), s = 2

 

 

 

cool cool cool

CPhill  Mar 11, 2017
 #1
avatar+2765 
0

Where is says " r s and are constants", it's actually " r and s are constants

tertre  Mar 11, 2017
 #2
avatar+87334 
+5
Best Answer

x^2 + 2sqrt(3)x + 1  = 0

 

x^2 + 2sqrt(3)x  = - 1         

 

Take (1/2) of 2sqrt(3)  = sqrt(3)....square this = 3   add to both sides

 

x^2 + 2sqrt(3)x + 3 =  -1 + 3      simpify and factor

 

(x  + sqrt(3) )^2   =    2

 

r =  sqrt(3), s = 2

 

 

 

cool cool cool

CPhill  Mar 11, 2017
 #3
avatar+2765 
+5

Thanks so much!

tertre  Mar 11, 2017

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