+1164 The polynomial \(p(x) = x^2+ax+b\) has distinct roots \(2a\) and \(2b\). Find \(a+b\).
+2668 By Vieta's, we have:
\(-a = 2a + 2b\) (i)
\(b = 4ab\) (ii)
From the second equation, we have \(a = {1 \over 4}\).
Subbing this into (i) gives us \(b = -{3 \over 8}\)
Thus, \(a + b = {1 \over 4} - {3 \over 8} = \color{brown}\boxed{-{1 \over 8}}\)
