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(x-4)(x-3)(x+10) 0

2 min read Jun 17, 2024
(x-4)(x-3)(x+10) 0

Solving the Equation (x-4)(x-3)(x+10) = 0

This equation involves a product of three factors equaling zero. This is a classic example of the Zero Product Property, which states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Let's break it down:

  1. Identify the factors: We have three factors: (x-4), (x-3), and (x+10).

  2. Apply the Zero Product Property: For the product to be zero, at least one of these factors must equal zero.

  3. Solve for x:

    • (x-4) = 0 => x = 4
    • (x-3) = 0 => x = 3
    • (x+10) = 0 => x = -10

Therefore, the solutions to the equation (x-4)(x-3)(x+10) = 0 are x = 4, x = 3, and x = -10.

Visualizing the Solution

We can visualize this solution graphically by plotting the function f(x) = (x-4)(x-3)(x+10). The x-intercepts of the graph represent the solutions to the equation f(x) = 0. You'll find the graph crosses the x-axis at x = 4, x = 3, and x = -10.

Key Points

  • The Zero Product Property is a fundamental principle in algebra, allowing us to solve equations where a product equals zero.
  • Understanding this property enables you to find the roots of polynomial equations.
  • Visualizing the solutions graphically helps reinforce the concept.

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