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Let r and s be the roots of 3x^2 + 4x + 12 = x^2 + 5x + 1. Find r^2 + s^2.

 
 Feb 23, 2021
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$2x^2-x+11=0$

$r^2+s^2=(r+s)^2-2rs$

By Vieta: $r+s=\frac{1}{2}, rs=\frac{11}{2}$

Answer: $\frac{1}{4}-11=\boxed{\frac{-43}{4}}$.

 
 Feb 23, 2021

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