>>13060580Suppose there were a rational zero x=p/q with gcd(p,q)=1 then
(p/q)^2 + M (p/q) + N = 0
p^2 + M p q + N q^2 = 0
Case 1: p is even then we would have
EVEN + EVEN + N q^2 = 0
which would imply that q is even to but that's a contradiction to gcd(p,q) = 1
Case 2: p is odd and q is odd then we would have
ODD + ODD + ODD = 0
which is a contradiction.
Case 3: p is odd and q is even then we would have
ODD + EVEN + EVEN = 0
which is also a contradiction.
Therefore our assumption must have been wrong and there is no rational zero.
