The roots of the equation 64x^2 - 16x + 1 = 0 are determined by the discriminant. In this case, the discriminant is 0, indicating there is one real, double root. Therefore, the correct answer is B.
To determine the nature of the roots of the quadratic equation 64x²-16x + 1 = 0, we need to use the discriminant. The discriminant is given by the formula b² - 4ac.
In the equation 64x²-16x + 1 = 0, the coefficients are a = 64, b = -16, and c = 1. Plugging these values into the discriminant formula:
b² - 4ac = (-16)² - 4(64)(1) = 256 - 256 = 0
Since the discriminant is 0, there is one real, repeated root.
Therefore, the correct answer is B) There is one real, double root