Final answer:
The discriminant of the quadratic equation x² - 3x + 3 = 0 is calculated using the formula b² - 4ac, resulting in -3, which indicates the equation has no real solutions.
Step-by-step explanation:
The discriminant of a quadratic equation of the form ax² + bx + c = 0 is given by the expression b² - 4ac. For the equation x² - 3x + 3 = 0, the coefficients are a = 1, b = -3, and c = 3. To find the discriminant, we plug these values into the formula, getting (-3)² - 4(1)(3), which simplifies to 9 - 12, resulting in a discriminant of -3. This negative value indicates that the quadratic equation has no real solutions but rather two complex solutions.