(m-1)^2 0

2 min read Jun 16, 2024
(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

  1. Take the square root of both sides: √((m-1)^2) = √0
  2. Simplify: This gives us (m-1) = 0
  3. 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.

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