Final answer:
The discriminant of the quadratic equation 5x² + 2x - 1 = 0 is 24, corresponding to the standard discriminant formula Δ = b² - 4ac.
Step-by-step explanation:
To determine the discriminant of the quadratic equation 5x² + 2x - 1 = 0, we must identify the coefficients corresponding to a, b, and c in the standard form of a quadratic equation, which is ax² + bx + c = 0. For this equation, a = 5, b = 2, and c = -1.
The formula for the discriminant (Δ) of a quadratic equation is Δ = b² - 4ac. Substituting our values into this formula, we get :
Δ = (2)² - 4(5)(-1)
Δ = 4 + 20
Δ = 24
Therefore, the discriminant of the given quadratic equation is 24, which means the correct answer is option (d).