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Solve this task!

 

(It comes from the 60th Mathematical Olympiad 2020 from classes 12-13 with solutions...it is a book)

 

niveau 9: 

 

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.

 
 Oct 13, 2021

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