Final answer:
The discriminant of the quadratic equation 0 = 6x² - 5x + 4 is calculated by plugging the coefficients into the formula D = b² - 4ac, yielding a discriminant of -71, which indicates two complex solutions.
Step-by-step explanation:
To calculate the discriminant of the quadratic equation 0 = 6x² - 5x + 4, we use the formula for the discriminant which is D = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax² + bx + c = 0. In this equation, a is 6, b is -5, and c is 4. Plugging these into the formula, we get:
D = (-5)² - 4(6)(4)
D = 25 - 96
D = -71
The discriminant is -71, which indicates that the quadratic equation has two complex solutions as the discriminant is less than zero.