## Understanding (m-1)^2 = 0

The equation **(m-1)^2 = 0** is a simple quadratic equation. Let's break down how to solve it and understand its significance.

### Solving the Equation

**Take the square root of both sides:**√((m-1)^2) = √0**Simplify:**This gives us (m-1) = 0**Solve for m:**Add 1 to both sides: m = 1

Therefore, the solution to the equation (m-1)^2 = 0 is **m = 1**.

### Significance of the Solution

The solution m = 1 has a couple of important implications:

**Double Root:**The equation (m-1)^2 = 0 represents a quadratic equation where the root**m = 1**is a**double root**. This means the solution appears twice in the factorization of the equation.**Vertex of a Parabola:**If we consider the equation as a function of m, f(m) = (m-1)^2, it represents a parabola. The solution m = 1 corresponds to the**vertex**of this parabola, which is the point where the function reaches its minimum value (in this case, 0).

### Summary

The equation (m-1)^2 = 0 is a simple quadratic equation with a single solution, m = 1. This solution represents a double root and corresponds to the vertex of the parabola represented by the function f(m) = (m-1)^2.