cubic equation

[stuart clark]

Let \(\displaystyle f(x)\) be a function defined on \(\displaystyle [-2009,2009]\) such that \(\displaystyle f(x)\) is Irrational \(\displaystyle \forall x\in \left[-2009,2009\right]\) and \(\displaystyle f(0)=2+\sqrt{2}+\sqrt{5}\).Then the equation \(\displaystyle f(2002)x^2+2.f(0)x+f(2009) = 0\) has only

Ans: (i) only Rational Roots

(ii) only Irrational roots.

(iii) one Rational one irrational roots

(iv) imaginary Roots.

 

[tkhunny]

Do we lose generality if we assume "is irrational" means \(\displaystyle \sqrt{7}\)?