Hello,

for the number (1), consider the discriminant of the quadratic equation : if it is strictly positive, then the quadratic will have two distinct real roots.

For the number (2), work around the discriminant : if it is a perfect square, the equation will have rational roots, and if the leading coefficient of is equal to 1, then the roots will actually be integers. Prove this by using the quadratic formula and showing that the upper part of the fraction is always even (therefore dividing it by two yields an integer).

Does it make sense ?