The answer is real, ℝ.
The discriminant [tex]b^2-4ac[/tex] is the thing under the square root (called the radicand) in the quadratic formula. When the discriminant is positive, we have a real solution, because the square root of a positive number gives two real solutions. When the discriminant is zero, we still get a real solution, but there's just one solution—zero. When the discriminant is negative, we get two complex solutions, because the square root of a negative number gives an imaginary solution.
