Final answer:
The equation 4n^2 - 8n + 4 = 0 is a quadratic equation solved using the quadratic formula. The discriminant is 0, indicating one real, repeated solution for n, which is n = 1. Thus, the roots are of the repeated or double type.
Step-by-step explanation:
The given equation 4n2 - 8n + 4 = 0 is a quadratic equation, which is of the general form at2 + bt + c = 0. To solve for n, we use the quadratic formula:
n = (-b ± √(b2 - 4ac)) / (2a)
Here, a = 4, b = -8, and c = 4. We can calculate the discriminant (√(b2 - 4ac)) which in this case is √((-8)2 - 4*4*4) = √(64 - 64) = √(0) = 0. Since the discriminant is 0, it means there is one real, repeated solution for n, which is found by plugging the values of a, b, and c into the quadratic formula.
Thus, the solution is:
n = (-(-8) ± √(0)) / (2*4)
n = (8 ± 0) / 8
n = 1
So the equation has one real solution, and the type of the roots is called a repeated or double root.