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The polynomial \(p(x) = x^2+ax+b\) has distinct roots \(2a\) and \(2b\). Find \(a+b\).

 Jul 4, 2022
 #1
avatar+2275 
+1

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, \(a + b = {1 \over 4} - {3 \over 8} = \color{brown}\boxed{-{1 \over 8}}\)

 Jul 4, 2022
 #2
avatar+1105 
+11

omg! nicely done! thx a lot! laugh

nerdiest  Jul 4, 2022
 #3
avatar+2275 
+1

No worries!!! smiley

BuilderBoi  Jul 4, 2022

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