+677 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.
