(x-1)(x-6) 0

Jasonbradley

2 min read

·

Jun 17, 2024

12

Share

Solving the Equation (x-1)(x-6) = 0

This equation represents a quadratic equation in factored form. To solve for the values of x that satisfy this equation, we can use 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 the equation:

1. Identify the factors: The equation is already factored into (x-1) and (x-6).
2. Apply the Zero Product Property: Set each factor equal to zero:
   • x - 1 = 0
   • x - 6 = 0
3. Solve for x:
   • x = 1
   • x = 6

Therefore, the solutions to the equation (x-1)(x-6) = 0 are x = 1 and x = 6.

Understanding the Concept:

• The equation (x-1)(x-6) = 0 represents a parabola that intersects the x-axis at two points: x = 1 and x = 6.
• These points are the roots or zeros of the equation.
• The factored form of the equation makes it easy to identify the roots directly.

In summary:

The equation (x-1)(x-6) = 0 has two solutions: x = 1 and x = 6. These solutions represent the x-intercepts of the parabola represented by the equation.