Final answer:
The discriminant of the function f(x) = 4x² - 7x - 5 is 129, which does not match any of the given options.
Step-by-step explanation:
The discriminant of a quadratic function is given by the formula Δ = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
In this case, the equation is f(x) = 4x² - 7x - 5, so a = 4, b = -7, and c = -5.
Substituting these values into the formula, we get Δ = (-7)² - 4(4)(-5) = 49 + 80 = 129.
The discriminant is 129, so none of the given options (a) 1, b) 36, c) -39, d) 49) match the discriminant value.