Let r and s be the roots of 3x^2 + 4x + 12 = x^2 + 5x + 1. Find r^2 + s^2.
$2x^2-x+11=0$
$r^2+s^2=(r+s)^2-2rs$
By Vieta: $r+s=\frac{1}{2}, rs=\frac{11}{2}$
Answer: $\frac{1}{4}-11=\boxed{\frac{-43}{4}}$.
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