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Let $r$ and $s$ be the roots of $3x^2 + 4x + 12 = 0.$ Find $r^2 + s^2.$

 Apr 24, 2020
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3x2 + 4x + 12  =  0 

 

Using the quadratic formula with  a = 3   b = 4   c = 12:

x  =  [ -4 +/- sqrt( 42 - 4·3·12 ) ] ( 2·3 )  =  ( -2 + 4sqrt(2) ) / 3      ( -2 - 4sqrt(2) ) / 3

[ ( -2 + 4sqrt(2) ) / 3 ]2  +  [  ( -2 - 4sqrt(2) ) / 3 ]2  

=  ( 36 - 16sqrt(2) ) / 9  +  ( 36 + 16sqrt(2) ) / 9  =  8

 Apr 24, 2020

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