Final answer:
The discriminant of the quadratic equation -x^2 - x - 5 = 0 is -19, indicating that there are two complex solutions for this equation.
Step-by-step explanation:
To find the discriminant of the quadratic equation -x^2 - x - 5 = 0, we can use the discriminant formula from the quadratic formula D = b^2 - 4ac, which helps us determine the nature and number of solutions of the quadratic equation ax^2+bx+c = 0. In this equation, a = -1, b = -1, and c = -5.
Now we substitute these values into the discriminant formula:
D = (-1)^2 - 4*(-1)*(-5)
D = 1 - 4*5
D = 1 - 20
D = -19
The discriminant D for the quadratic equation -x^2 - x - 5 = 0 is -19. Because the discriminant is a negative number, we can conclude that the quadratic equation has two complex solutions.