What are the roots of x^2 - 4x + 4 = 0?

• A. x=0
• B. x=4
• C. no real roots
• D. x=2

Answer: (D)

The quadratic is a perfect square: x^2 - 4x + 4 = (x - 2)^2. When a squared expression equals zero, the value inside the square must be zero, so x - 2 = 0, giving x = 2. This is a double root, since the squared term vanishes only at that one value. The discriminant confirms this: 16 - 16 = 0, so there is exactly one real root, x = 2.