Multiple choice

The difference of roots of the quadratic equation $4y^2 - 4y + 1 = 0$ is _________.

  1. 0

  2. 1
  3. $\displaystyle - \frac{1}{2}$

  4. 2
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A Correct answer
Explanation

The equation 4y^2 - 4y + 1 = 0 is (2y - 1)^2 = 0. The roots are 1/2 and 1/2. The difference is 1/2 - 1/2 = 0.

AI explanation

The given quadratic equation is 4y^2 - 4y + 1 = 0, which factors into the perfect square (2y - 1)^2 = 0. Taking the square root of both sides gives 2y - 1 = 0, meaning y = 1/2 is a double root. Since both roots are equal to 1/2, their difference is 1/2 - 1/2 = 0.

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