Fun with quadratics

Algebra Level 3

Consider the quadratic polynomial \(f(x)=a{ x }^{ 2 }+bx+c\) (\(a\neq 0\)).

It's given that \(a\lt b\) and for every real \(x\), we have \(f(x)\geq 0\).

Find the minimum possible value of \(\dfrac{ a+b+c }{ b-a }\) .

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