# Family Functions Related to Phi

Algebra Level 3

Let $$f_n(x)$$ be a family of quadratics with integer coefficients in the form $$ax^2+bx+c$$ such that at least one of its roots is $$\phi$$, which is $$\frac{1+\sqrt{5}}{2}$$. There exists a quadratic in the family $$f_n(x)$$ such that the sum $$a+b+c=-1$$. The name of this particular function is $$f_{\star}(x)$$. Find $$f_{\star}(16)$$.

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