Question
What values of \( a \) satisfy the equation \( (a - 5)(a + 1) = 0 \)?
Ask by Chandler Williams. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The values of \( a \) that satisfy the equation are \( a = 5 \) and \( a = -1 \).
Solution
To solve the equation \( (a - 5)(a + 1) = 0 \), we can use the **Zero Product Property**. 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 apply it step by step:
1. **Set Each Factor Equal to Zero:**
\[
a - 5 = 0 \quad \text{or} \quad a + 1 = 0
\]
2. **Solve Each Equation Individually:**
- For \( a - 5 = 0 \):
\[
a = 5
\]
- For \( a + 1 = 0 \):
\[
a = -1
\]
3. **Combine the Solutions:**
The values of \( a \) that satisfy the original equation are:
\[
a = 5 \quad \text{and} \quad a = -1
\]
**Conclusion:**
The equation \( (a - 5)(a + 1) = 0 \) is satisfied when \( a = 5 \) or \( a = -1 \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To solve the equation \( (a - 5)(a + 1) = 0 \), we can apply the Zero Product Property, which states that if the product of two factors is zero, at least one of the factors must be zero. This gives us two equations to solve: 1. \( a - 5 = 0 \) 2. \( a + 1 = 0 \) Solving the first equation: \[ a - 5 = 0 \quad \Rightarrow \quad a = 5 \] For the second equation: \[ a + 1 = 0 \quad \Rightarrow \quad a = -1 \] So, the values of \( a \) that satisfy the equation are \( a = 5 \) and \( a = -1 \).
