Final answer:
The discriminant of the equation a^2 - 2a - 5 = 0 is calculated using the formula d = b^2 - 4ac, which yields the value of 24.
Step-by-step explanation:
The discriminant (d) of a quadratic equation ax^2 + bx + c = 0 is given by the formula d = b^2 - 4ac. In the given equation, a^2 - 2a - 5 = 0, we identify a = 1, b = -2, and c = -5. Substituting these values into the discriminant formula gives us:
d = (-2)^2 - 4(1)(-5) = 4 + 20 = 24
Therefore, the discriminant of the equation a^2 - 2a - 5 = 0 is 24.