(x+3)(x-5)=0 Quadratic Equation

3 min read Jun 16, 2024

Solving the Quadratic Equation: (x+3)(x-5) = 0

This article will guide you through solving the quadratic equation (x+3)(x-5) = 0. We'll explore the concepts behind this type of equation and break down the steps for finding its solutions.

Understanding the Equation

The equation (x+3)(x-5) = 0 represents a quadratic equation in factored form. Here's why:

Quadratic Equation: A quadratic equation is an equation of the form ax² + bx + c = 0, where 'a', 'b', and 'c' are constants and 'a' is not equal to 0.
Factored Form: When a quadratic equation is written as a product of two linear expressions, like (x+3)(x-5), it's in factored form.

The Zero Product Property

The key to solving this equation lies in the Zero Product Property. This property states:

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 this to our equation:

If (x+3)(x-5) = 0, then either (x+3) = 0 or (x-5) = 0 (or both).

Solving for x

Now, we can solve each of the linear equations:

x + 3 = 0
- Subtract 3 from both sides: x = -3
x - 5 = 0
- Add 5 to both sides: x = 5

The Solutions

Therefore, the solutions to the quadratic equation (x+3)(x-5) = 0 are:

x = -3
x = 5

These solutions represent the x-intercepts of the parabola represented by the quadratic equation.

In Summary

By utilizing the Zero Product Property, we successfully solved the quadratic equation (x+3)(x-5) = 0, finding two distinct solutions: x = -3 and x = 5. This process highlights the importance of recognizing factored forms of quadratic equations and how they simplify the solution process.