(x-4)*(x-9)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-4)(x-9) = 0

This equation is a quadratic equation in factored form. To find the solutions (also known as roots or zeros) of this equation, we can use the Zero Product Property:

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

Applying this to our equation, we have:

(x - 4) = 0 or (x - 9) = 0

Now we solve each equation individually:

• x - 4 = 0
  Adding 4 to both sides:
  x = 4

• x - 9 = 0
  Adding 9 to both sides: x = 9

Therefore, the solutions to the equation (x-4)(x-9) = 0 are x = 4 and x = 9.

In other words, the values x = 4 and x = 9 make the equation true.

Explanation

The equation (x-4)(x-9) = 0 represents a parabola that intersects the x-axis at the points x = 4 and x = 9. These points are the roots of the equation, where the value of the equation is zero.

Key takeaways:

• Factoring a quadratic equation is a powerful tool to find its solutions.
• The Zero Product Property is crucial for solving equations in factored form.
• The solutions of a quadratic equation represent the points where the graph of the equation intersects the x-axis.