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We consider the set of functions given by 

 

\(\int a (x) = (x-a)^2 + (4a^2-12a) \)

 

 the equation with real parameter a.

 

a) Determine all those values for a for which the function \(\int a (x)\) has exactly two different zeros.

 

b) Among all the values for a for which the function \(\int a (x)\) has exactly two different zeros, determine those for which the distance between these zeros is maximum.

 
 Jan 22, 2022

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