Is it possible to construct a polynomial of degree `N`, with all of them as integer coefficient have a `root` as the given value. The root value provided is not necessarily a rational number.


For example, if the root is `28.552622898861801` we can have a polynomial of degree 10 whose one root will be the given value.


`10000 x^10 - 280000 x^9 - 150000 x^8 - 220000 x^7 - 40000 x^6 - 790000 x^5 - 160000 x^4 - 320000 x^3 - 270000 x^2 - 250000 x - 251271 = 0` 


[Wolfram alpha link for this equation](http://www.wolframalpha.com/input/?i=10000+x%5E10+-+280000+x%5E9+-+150000+x%5E8+-+220000+x%5E7+-+40000+x%5E6+-+790000+x%5E5+-+160000+x%5E4+-+320000+x%5E3+-+270000+x%5E2+-+250000+x+-+251271+%253D+0)



Polynomial of degree N with integer coefficient for a given root.
The problem can be solved by running some Integer Relation algorithm (e.g., PSLQ) on the numbers $1, r, r^2, \dots, r^N$ where $r$ is a given root.


See <http://en.wikipedia.org/wiki/Integer_relation_algorithm>


For example, here is computation in PARI/GP which gives a better result than the polynomial shown in question: 


? r = 28.552622898861801; algdep(r,10)


%1 = 3\*x^10 + 38\*x^9 - 3695\*x^8 + 4582\*x^7 + 3016\*x^6 + 1435\*x^5 + 4552\*x^4 - 1219\*x^3 - 9920\*x^2 - 2402\*x + 3087


? subst(%1,x,r)


%2 = -2.7334689816478450022 E-24


