Being a positive real number and not-null, consider the functions....?

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Being a positive real number and not-null, consider the functions:

f: R --> R; f(x) = ax² + 2 e g : [2;1) --->R+; g(x) = sqrt[(x-2)/a]

Their graphics on a cartesian plan intercept only at two distinct points M and N.

(a)Determine the minor real interval in which the number (a) is necessarily contained.
(b)Knowing this way between M and N 3.sqrt(2) determine the value of (a).
 
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