Jasonbradley
Home

(x-2)(x-3)(x-4) 0

2 min read Jun 17, 2024
(x-2)(x-3)(x-4) 0

Solving the Equation (x-2)(x-3)(x-4) = 0

This equation represents a cubic polynomial. To solve for the values of x that satisfy this equation, we can use the following principle:

The Zero Product Property

This property states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero.

Applying the Property

In our case, we have three factors: (x-2), (x-3), and (x-4). To make the product equal to zero, at least one of these factors must be zero.

Therefore, we have three possible scenarios:

  1. (x-2) = 0 Solving for x, we get x = 2

  2. (x-3) = 0 Solving for x, we get x = 3

  3. (x-4) = 0 Solving for x, we get x = 4

Solutions

Therefore, the solutions to the equation (x-2)(x-3)(x-4) = 0 are x = 2, x = 3, and x = 4.

Graphical Representation

The graph of the function y = (x-2)(x-3)(x-4) would intersect the x-axis at these three points, confirming our solutions.

Note: This method of solving polynomial equations by factoring and applying the Zero Product Property is a fundamental technique in algebra. It allows us to find the roots of the equation, which represent the values of x where the function crosses the x-axis.

Featured Posts