(2x-5)(7x+2)=0

Jasonbradley

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Jun 16, 2024

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Solving the Equation (2x-5)(7x+2) = 0

This equation is a quadratic equation in factored form. We can use the Zero Product Property to solve it. This property states that if the product of two factors is zero, then at least one of the factors must be zero.

Here's how to solve it:

1. Set each factor equal to zero:

   • 2x - 5 = 0
   • 7x + 2 = 0

2. Solve each equation for x:

   • 2x = 5
   • x = 5/2
   • 7x = -2
   • x = -2/7

Therefore, the solutions to the equation (2x-5)(7x+2) = 0 are x = 5/2 and x = -2/7.

Understanding the Zero Product Property

The Zero Product Property is a fundamental concept in algebra. It allows us to solve equations by breaking them down into simpler equations. In this case, instead of dealing with a complex quadratic equation, we solved two simple linear equations.

Visualizing the Solutions

The solutions x = 5/2 and x = -2/7 represent the x-intercepts of the graph of the quadratic function y = (2x-5)(7x+2). These are the points where the graph crosses the x-axis.

Key Takeaways

• The Zero Product Property is a powerful tool for solving equations.
• Factored quadratic equations can be solved easily using this property.
• The solutions to a quadratic equation represent the x-intercepts of its graph.