Find a polynomial of degree $8$ with integer coefficients with given root

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algorithm to find a polynomial $f(x)$ s.t

(1) $degree(f(x))<9$

(2) Integer coefficients

(3) Absolute value of coefficients $< 10^5$

(4) f(39.770525) =~ 0 about to be <<10^-10

I heard that it is similar to coppersmith algorithm, but I can't find why