Comprehension: \( \quad: \) Let \( f(x)=x^{2}+a x+b \) is a function \( a, b \in R, a^{2}4 b \) ...

Comprehension: \( \quad: \) Let \( f(x)=x^{2}+a x+b \) is a function \( a, b \in R, a^{2}4 b \) and \( g(x)=x^{2}+2 x-1 \) such that \( f\left(g\left(x_{i}\right)\right) \) \( =0 \forall i \in\{1,2,3,4\} \) and \( x_{i}x_{\mathrm{i}}+1 \forall i=1,2,3 \) and \( x_{1}, x_{2}, x_{3}, x_{4} \) are for an Arithmetic Progression, then
The values of \( |\mathrm{a}| \) when \( (a-b) \) at its maximum value