Prove that if p and q are rational and p is not equal to 0, the roots of the quadratic equations p x(square) + 2qx -p +2q = 0 are rational.
the discriminant is
4q^2 - 4p(2q-p)
= 4q^2 - 8pq + 4p^2
= 4(q-p)^2
which is a perfect square. Consider that in the light of the quadratic formula, and the result is clear.