Discriminant of a Quadratic Equation - Definition & Examples

Galois is trying to write questions for his algebra class with nice answers without radicals. He finds a list of quadratics $ax^2 + bx + c$ with integer coefficients, whose roots are either integers or fractions (so they can be written without square roots or $i = \sqrt{-1}$). Which of the following numbers are possible discriminants of the quadratics on his list?