(x-5)(x-7)=0 Lớp 6

Jasonbradley

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Jun 17, 2024

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Solving Equations: (x - 5)(x - 7) = 0

This equation presents a simple yet fundamental concept in algebra: the Zero Product Property. This property states that if the product of two or more factors is equal to zero, then at least one of the factors must be zero.

Let's break down the equation:

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

We have two factors: (x - 5) and (x - 7). For their product to be zero, one or both of these factors must equal zero.

Step 1: Set each factor equal to zero.

• x - 5 = 0
• x - 7 = 0

Step 2: Solve for x in each equation.

• x - 5 = 0
  Adding 5 to both sides: x = 5

• x - 7 = 0 Adding 7 to both sides: x = 7

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

Key takeaways:

• The Zero Product Property is crucial for solving equations with multiple factors.
• By setting each factor to zero, we can find all possible solutions.
• This concept is fundamental in understanding polynomial equations and other algebraic concepts.