MathDB

32

Part of 2004 National Olympiad First Round

Problems(1)

P32 [Algebra] - Turkish NMO 1st Round - 2004

Source:

11/16/2013
If aa and bb are the roots of the equation x2−2cx−5d=0x^2-2cx-5d = 0, cc and dd are the roots of the equation x2−2ax−5b=0x^2-2ax-5b=0, where a,b,c,da,b,c,d are distinct real numbers, what is a+b+c+da+b+c+d?
<spanclass=′latex−bold′>(A)</span> 10<spanclass=′latex−bold′>(B)</span> 15<spanclass=′latex−bold′>(C)</span> 20<spanclass=′latex−bold′>(D)</span> 25<spanclass=′latex−bold′>(E)</span> 30 <span class='latex-bold'>(A)</span>\ 10 \qquad<span class='latex-bold'>(B)</span>\ 15 \qquad<span class='latex-bold'>(C)</span>\ 20 \qquad<span class='latex-bold'>(D)</span>\ 25 \qquad<span class='latex-bold'>(E)</span>\ 30