Pregunta
What values of \( a \) satisfy the equation \( (a - 5)(a + 1) = 0 \)?
Ask by Fernandez Norris. in Egypt
Jan 24,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
The values of \( a \) that satisfy the equation are \( a = 5 \) and \( a = -1 \).
Solución
To find the values of \( a \) that satisfy the equation:
\[
(a - 5)(a + 1) = 0
\]
we can use the **Zero Product Property**, which states that if the product of two factors is zero, then at least one of the factors must be zero.
So, set each factor equal to zero and solve for \( a \):
1. **First Factor:**
\[
a - 5 = 0 \\
\Rightarrow a = 5
\]
2. **Second Factor:**
\[
a + 1 = 0 \\
\Rightarrow a = -1
\]
**Conclusion:**
The values of \( a \) that satisfy the equation are:
\[
a = 5 \quad \text{and} \quad a = -1
\]
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Simplifique esta solución Mind Expander
To solve the equation \( (a - 5)(a + 1) = 0 \), we can use the zero product property, which states that if the product of two factors is zero, at least one of the factors must be zero. Setting each factor equal to zero gives us two equations to solve: 1. \( a - 5 = 0 \) 2. \( a + 1 = 0 \) Solving the first equation: - \( a - 5 = 0 \) - Adding 5 to both sides, we find \( a = 5 \). Solving the second equation: - \( a + 1 = 0 \) - Subtracting 1 from both sides, we find \( a = -1 \). Therefore, the values of \( a \) that satisfy the equation \( (a - 5)(a + 1) = 0 \) are \( a = 5 \) and \( a = -1 \).
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