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Find the sum of the squares of the roots of 3x^2 + 4x + 12 = 0.

 

thanks !

 Mar 23, 2020
 #1
avatar+111330 
+2

Call the roots a, b

 

The  sum of  the  roots  =   -4/3

So

a + b = -4/3      square both sides  of this

a^2 + 2ab + b^2  = 16/9     (1)

 

The product of the roots =  12/3  = 4

So

ab = 4    

And

2ab  =8      (2)

 

Sub (2)  into (1)  and we have that

 

a^2  + 8  + b^2  =  16/9

 

a^2 + b^2  =  16/9  - 8

 

a^2  + b^2 =  16/9 - 72/9

 

a^2  + b^2   =  [ 16 - 72 ] / 9

 

a^2 + b^2 =  -56 /9

 

 

 

 

cool cool cool

 Mar 23, 2020
 #2
avatar+1970 
+2

I agree! Nice job, Chris!

CalTheGreat  Mar 23, 2020
 #3
avatar+104 
0

thanks !! :))

matthewmacdell  Mar 23, 2020

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