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r and s are the roots of 3x^2 + 4x - 12 = 0. Find r^2+s^2+2rs

 Jan 21, 2022
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Divide 3x2+4x12=0 by 3:  x2+43x4=0   ...(1)

 

Quadratic with roots r and s:  (xr)(xs)=0  or  x2(r+s)x+rs=0    ...(2)

 

Compare (1) and (2)  to see that r+s=43    ...(3)

 

Note that r2+s2+2rs=(r+s)2

 

Now it should be easy to answer the question.

 Jan 21, 2022

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