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
proof for quadratics by xdog)
I was a little sceptical, but I see that xdog is right.
Odd squares = 1 mod 8
Even squares = 0 or 4 mod 8
If a and c are odd integers, 4ac = 4 mod 8.
b^2 - 4ac = 5 mod 8, so D is not a an odd or an even square, so the equation has no rational roots.
re: proof for quadratics
