Let the roots of f(x)=x be α and β where f(x) is a quadratic polynomial. It is true that α,β also satisfies f(f(x))=x. Let the other roots of the eqn. f(f(x))=x be γ and δ. Now Correct statements are:
23take a standard quadratic f(x)=ax2+bx+c
f(x)=x
ax2+bx+c=x
i.e ax2+(b-1)x+c=0
the roots of dis eqn are alpha and beta.
now find f(f(x)) by replacing x by f(x)i.e by replacing x by ax2+bx+c
i think so this is how it shud be done ..but its a very lengthy method, there is suerly another method to it ...
33Its discussion is here:
http://targetiit.com/iit-jee-forum/posts/biquadratic-2135.html
and grandmaster correct statements are?:
a) If α β are real and distinct then γ and δ are not real.
b) If α+β=γ+δ then none of α β γ δ are real.
c) If α=β(real) then γ and δ are real.
d) None
ans :b
