# Weird Polynomial Relation

Algebra Level 3

Let $$P(x)$$ a polynomial in $$x$$ with real coefficients such that for all real numbers $$x, y, z$$ satisfying $$xy+yz+zx=1,$$ $P(x)+P(y)+P(z)=P(x+y+z).$ Furthermore, $$P(0)=1$$ and $$P(1)=4.$$ What is the value of $$\sqrt{P(2017)}?$$

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