Question

You can determine by the discriminant whether the solutions to the equation are _____ or complex numbers.

Answer 1

The answer is real, ℝ. 

The discriminant  $b^2-4ac$ 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.