+678 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.
