(x-7)(x-3)=0

Jasonbradley

2 min read

·

Jun 17, 2024

12

Share

Solving the Equation (x-7)(x-3) = 0

This equation represents a simple quadratic equation that can be solved using the Zero Product Property. This property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Here's how to solve it:

1. Identify the factors: The equation is already factored: (x-7)(x-3) = 0. The factors are (x-7) and (x-3).

2. Apply the Zero Product Property: Since the product of these factors is zero, either (x-7) = 0 or (x-3) = 0.

3. Solve for x:

   • If (x-7) = 0, then x = 7.
   • If (x-3) = 0, then x = 3.

Therefore, the solutions to the equation (x-7)(x-3) = 0 are x = 7 and x = 3.

Understanding the Solution

The equation represents a parabola that intersects the x-axis at the points x = 7 and x = 3. These points are called the roots or zeros of the equation.

In summary:

• The Zero Product Property is a powerful tool for solving quadratic equations in factored form.
• The solutions to the equation (x-7)(x-3) = 0 are x = 7 and x = 3.
• These solutions represent the x-intercepts of the parabola represented by the equation.