(x-3)(x-2)=0

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

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

This equation represents a simple quadratic equation in factored form. Let's explore how to solve it:

Understanding the Zero Product Property

The equation relies on the Zero Product Property, which states:

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

In our case, the factors are (x - 3) and (x - 2). To make the product equal to zero, one or both of these factors must equal zero.

Solving for x

  • Factor 1: (x - 3) = 0

    • Add 3 to both sides: x = 3
  • Factor 2: (x - 2) = 0

    • Add 2 to both sides: x = 2

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

Interpretation

These solutions represent the x-intercepts of the quadratic function represented by the equation. In other words, the graph of the function crosses the x-axis at the points x = 3 and x = 2.

Conclusion

By understanding the Zero Product Property, we can easily solve factored quadratic equations like (x - 3)(x - 2) = 0. This property allows us to find the values of x that make the equation true, which are the roots or solutions of the equation.

Related Post


Featured Posts