Final answer:
The nature of the roots for the quadratic equation 3x^2 - 6x + 3 = 0 is a unique real solution.
Step-by-step explanation:
The given quadratic equation is 3x^2 - 6x + 3 = 0. To determine the nature of its roots, we can use the discriminant formula: D = b^2 - 4ac. If D > 0, we have two distinct real solutions, if D = 0, we have a unique real solution, and if D < 0, we have no real solutions.
In this case, a = 3, b = -6, and c = 3. Plugging these values into the discriminant formula, we get D = (-6)^2 - 4(3)(3) = 0. Since the discriminant is equal to 0, the nature of the roots for this quadratic equation is a unique real solution (Option D).