Question

Suppose P(x) = x^3 + a x^2 + b x + c has three distinct integer roots. P(2002)=2001, q(x)=x^2-2x+2002 and P(q(x)) dosen't have a real roots. now find different two positve roots of p(x).

Answer 1

sorry, i misstyped the problem.

Answer 2

My prof told me that if we have p(2002) = 2001 it means 2002|P(x) = something and remainder is 2001
yours has "something " in the form of q (x) so I want to make sure our information and knowledge "meet " at somewhere.
discuss, please

Answer 3

you stated that P(x) has 3 distinct roots, and ask to find out the other two. but what is the first one? if P(2002) =2001 , then 2002 definitely is not a root. I want to know about that "real root"