Assume that p/q is a rational root of the equation with (p,q) = 1.
Then, ap2 + bpq + cq2 = 0. There are only three
for the integers p and q: both are odd or one is odd and
is even. In each of the three cases the sum of the three terms
bpq, and cq2 is odd. This contradicts the
assumption that the sum
should be even. Therefore, the equation has no rational root.
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