Roots of a Polynomial

[man111]

Let $f(x)$ be a function defined on $[-2009,2009]$ such that $f(x)$ is

Irrational $\forall x\in \left[-2009,2009\right]$ and $f(0)=2+\sqrt{2}+\sqrt{5}$.Then the

equation $f(2002)x^2+2.f(0)x+f(2009) = 0$has only

Ans: (i) only Rational Roots

(ii) only Irrational roots.

(iii) one Rational one irrational roots

(iv) imaginary Roots.

[Null]

Можно просто сказать $Ax^2+2(2+\sqrt{2}+\sqrt{5})x+B=0$, где $A, B$ - иррациональны?