# Inspired by Deepanshu Gupta

Algebra Level 5

$f(x)=x^4+ax^3+bx^2+cx+1$

If $$f(x)$$ has at least one real root, for real numbers $$a,b$$ and $$c$$, find the minimal value of $$a^2+b^2+c^2$$. Write your answer in the form $$\frac{p}{q}$$ for co-prime positive integers $$p$$ and $$q$$, and enter $$p+q$$.

If you come to the conclusion that no minimum is attained, enter 666.

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