Assume that p/q is a rational root of the equation with (p,q) = 1.
Then, ap^{2} + bpq + cq^{2} = 0. There are only three
possible cases
for the integers p and q: both are odd or one is odd and
the other
is even. In each of the three cases the sum of the three terms
ap^{2},
bpq, and cq^{2} is odd. This contradicts the
assumption that the sum
should be even. Therefore, the equation has no rational root.

Comments: (
You must be logged in to post comments.)