(x-10)(x-10)=

Jasonbradley

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Jun 17, 2024

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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.