(x-4)(x+5)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-4)(x+5)=0

This equation is a quadratic equation in factored form. Here's how to solve it and understand the concept:

Understanding Factored Form

The equation (x-4)(x+5)=0 is already factored, meaning it's expressed as a product of two expressions. The key to solving it lies in the Zero Product Property:

Zero Product Property: If the product of two or more factors is zero, then at least one of the factors must be zero.

Solving the Equation

1. Set each factor equal to zero:

   • x - 4 = 0
   • x + 5 = 0

2. Solve for x in each equation:

   • x = 4
   • x = -5

Solutions

Therefore, the solutions to the equation (x-4)(x+5)=0 are x = 4 and x = -5.

Visualizing the Solutions

These solutions represent the x-intercepts of the parabola represented by the quadratic equation. The graph intersects the x-axis at x = 4 and x = -5.

Importance of the Zero Product Property

The Zero Product Property is fundamental in solving quadratic equations. It allows us to break down a complex equation into simpler equations that are easier to solve. Understanding and applying this property is crucial for mastering algebraic manipulation and problem-solving.