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
Request for Clarification by H M)
From how I read the problem, x^2-1 is not a valid polynomial: the coefficient of the linear term is 0, which is even.
If our polynomial is a_(2k)*x^(2k) + a_(2k-1)*x^(2k-1) + ... + a_1*x + a_0, then all the coefficients {a_2k, a_2k-1, ..., a_1, a_0} are odd integers.
(Apologies for lack of proper subscripts and superscripts)
re: Request for Clarification
