For the quadratic equation x^2 + (1)x + 3 = 0, determine the nature of its roots.
Note
Think of this as a discriminant question. For a quadratic equation ax^2 + bx + c = 0, first identify a = 1, b = 1, and c = 3. Now calculate D = b^2 - 4ac = (1)^2 - 4(1)(3) = -11. Since D < 0, the equation has no real roots. A negative discriminant means the square root part of the quadratic formula is not real.
