(x-10)(x-10)=

2 min read Jun 17, 2024
(x-10)(x-10)=

Factoring and Solving (x-10)(x-10) = 0

The expression (x-10)(x-10) = 0 represents a quadratic equation in factored form. Here's a breakdown of how to factor, solve, and understand this equation:

Understanding the Factored Form

  • (x-10)(x-10) = 0 means that we are multiplying two expressions together and the result is zero.
  • The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Solving for x

To solve for x, we apply the Zero Product Property:

  1. Set each factor equal to zero:

    • x - 10 = 0
    • x - 10 = 0
  2. Solve for x in each equation:

    • x = 10
    • x = 10

The Solution

We find that the equation has a double root at x = 10. This means the solution x = 10 occurs twice.

Graphing the Equation

The equation (x-10)(x-10) = 0 represents a parabola that touches the x-axis at the point (10, 0). The vertex of the parabola is also located at (10, 0).

Key Points

  • Factored form makes solving quadratic equations easier by applying the Zero Product Property.
  • A double root indicates that the solution occurs twice.
  • The graph of a quadratic equation with a double root touches the x-axis at a single point, which is also the vertex of the parabola.

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