%5E2-0.jpeg "(m-1)^2 0")
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.