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

The answer is real, ℝ. 

The discriminant   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.

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