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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