P(x) is a polynomial of even degree. Also, all the coefficients of P(x) are odd numbers.
Is it possible for P(x) to have a rational root?
• If so, provide an example.
• If not, prove that it is NOT possible for P(x) to have a rational root.
(In reply to
Idea for a=1 by Jer)
I think Jer's proof is probably true, but I think we need to add a proof that "if the roots are rational they must be integers". That part is not immediately obvious to me. Why can't p and q be non-integers such that b=-(p+q) and c=pq?
re: Idea for a=1
