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Let \(a\) and \(b \) be constants. Suppose that the equation

                                                                                        \(\frac{(x+a)(x+b)(x+12)}{(x+3)^2} = 0\)

has exactly \(3 \) distinct roots, while the equation

                                                                                  \(\frac{(x+2a)(x+3)(x+6)}{(x+b)(x+12)} = 0\)

has exactly \(1 \) distinct root. Compute  \(100a+b\).

                              

 Nov 23, 2019
 #1
avatar+167 
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Can I get a detailed explanation... I have trouble these types of problems. I found 1 root for the 1st equation but none for the second. 

 Nov 23, 2019
edited by AoPS.Morrisville  Nov 23, 2019

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