IDNLearn.com is designed to help you find reliable answers quickly and easily. Discover the information you need from our experienced professionals who provide accurate and reliable answers to all your questions.
Sagot :
Let's solve each quadratic equation step by step to find the correct solution sets.
1. Equation: [tex]\(a^2 - 9a + 14 = 0\)[/tex]
To solve this, we can factorize the quadratic expression:
[tex]\[ a^2 - 9a + 14 = (a - 7)(a - 2) = 0 \][/tex]
Setting each factor to zero gives us:
[tex]\[ a - 7 = 0 \quad \text{or} \quad a - 2 = 0 \][/tex]
Thus, the solutions are:
[tex]\[ a = 7 \quad \text{and} \quad a = 2 \][/tex]
Solution set: [tex]\(\{7, 2\}\)[/tex]
2. Equation: [tex]\(a^2 + 9a + 14 = 0\)[/tex]
To solve this, we can factorize the quadratic expression:
[tex]\[ a^2 + 9a + 14 = (a + 7)(a + 2) = 0 \][/tex]
Setting each factor to zero gives us:
[tex]\[ a + 7 = 0 \quad \text{or} \quad a + 2 = 0 \][/tex]
Thus, the solutions are:
[tex]\[ a = -7 \quad \text{and} \quad a = -2 \][/tex]
Solution set: [tex]\(\{-7, -2\}\)[/tex]
3. Equation: [tex]\(a^2 + 3a - 10 = 0\)[/tex]
To solve this, we can factorize the quadratic expression:
[tex]\[ a^2 + 3a - 10 = (a + 5)(a - 2) = 0 \][/tex]
Setting each factor to zero gives us:
[tex]\[ a + 5 = 0 \quad \text{or} \quad a - 2 = 0 \][/tex]
Thus, the solutions are:
[tex]\[ a = -5 \quad \text{and} \quad a = 2 \][/tex]
Solution set: [tex]\(\{2, -5\}\)[/tex]
4. Equation: [tex]\(a^2 + 5a - 14 = 0\)[/tex]
To solve this, we can factorize the quadratic expression:
[tex]\[ a^2 + 5a - 14 = (a + 7)(a - 2) = 0 \][/tex]
Setting each factor to zero gives us:
[tex]\[ a + 7 = 0 \quad \text{or} \quad a - 2 = 0 \][/tex]
Thus, the solutions are:
[tex]\[ a = -4 \quad \text{and} \quad a = 2 \][/tex]
Solution set: [tex]\(\{2, -4\}\)[/tex]
5. Equation: [tex]\(a^2 - 5a - 14 = 0\)[/tex]
To solve this, we can factorize the quadratic expression:
[tex]\[ a^2 - 5a - 14 = (a - 7)(a + 2) = 0 \][/tex]
Setting each factor to zero gives us:
[tex]\[ a - 7 = 0 \quad \text{or} \quad a + 2 = 0 \][/tex]
Thus, the solutions are:
[tex]\[ a = 7 \quad \text{and} \quad a = -2 \][/tex]
Solution set: [tex]\(\{7, -2\}\)[/tex]
So, the correct matches are:
1. [tex]\(a^2 - 9a + 14 = 0 \quad \longrightarrow \quad \{7, 2\}\)[/tex]
2. [tex]\(a^2 + 9a + 14 = 0 \quad \longrightarrow \quad \{-7, -2\}\)[/tex]
3. [tex]\(a^2 + 3a - 10 = 0 \quad \longrightarrow \quad \{2, -5\}\)[/tex]
4. [tex]\(a^2 + 5a - 14 = 0 \quad \longrightarrow \quad \{2, -4\}\)[/tex]
5. [tex]\(a^2 - 5a - 14 = 0 \quad \longrightarrow \quad \{7, -2\}\)[/tex]
1. Equation: [tex]\(a^2 - 9a + 14 = 0\)[/tex]
To solve this, we can factorize the quadratic expression:
[tex]\[ a^2 - 9a + 14 = (a - 7)(a - 2) = 0 \][/tex]
Setting each factor to zero gives us:
[tex]\[ a - 7 = 0 \quad \text{or} \quad a - 2 = 0 \][/tex]
Thus, the solutions are:
[tex]\[ a = 7 \quad \text{and} \quad a = 2 \][/tex]
Solution set: [tex]\(\{7, 2\}\)[/tex]
2. Equation: [tex]\(a^2 + 9a + 14 = 0\)[/tex]
To solve this, we can factorize the quadratic expression:
[tex]\[ a^2 + 9a + 14 = (a + 7)(a + 2) = 0 \][/tex]
Setting each factor to zero gives us:
[tex]\[ a + 7 = 0 \quad \text{or} \quad a + 2 = 0 \][/tex]
Thus, the solutions are:
[tex]\[ a = -7 \quad \text{and} \quad a = -2 \][/tex]
Solution set: [tex]\(\{-7, -2\}\)[/tex]
3. Equation: [tex]\(a^2 + 3a - 10 = 0\)[/tex]
To solve this, we can factorize the quadratic expression:
[tex]\[ a^2 + 3a - 10 = (a + 5)(a - 2) = 0 \][/tex]
Setting each factor to zero gives us:
[tex]\[ a + 5 = 0 \quad \text{or} \quad a - 2 = 0 \][/tex]
Thus, the solutions are:
[tex]\[ a = -5 \quad \text{and} \quad a = 2 \][/tex]
Solution set: [tex]\(\{2, -5\}\)[/tex]
4. Equation: [tex]\(a^2 + 5a - 14 = 0\)[/tex]
To solve this, we can factorize the quadratic expression:
[tex]\[ a^2 + 5a - 14 = (a + 7)(a - 2) = 0 \][/tex]
Setting each factor to zero gives us:
[tex]\[ a + 7 = 0 \quad \text{or} \quad a - 2 = 0 \][/tex]
Thus, the solutions are:
[tex]\[ a = -4 \quad \text{and} \quad a = 2 \][/tex]
Solution set: [tex]\(\{2, -4\}\)[/tex]
5. Equation: [tex]\(a^2 - 5a - 14 = 0\)[/tex]
To solve this, we can factorize the quadratic expression:
[tex]\[ a^2 - 5a - 14 = (a - 7)(a + 2) = 0 \][/tex]
Setting each factor to zero gives us:
[tex]\[ a - 7 = 0 \quad \text{or} \quad a + 2 = 0 \][/tex]
Thus, the solutions are:
[tex]\[ a = 7 \quad \text{and} \quad a = -2 \][/tex]
Solution set: [tex]\(\{7, -2\}\)[/tex]
So, the correct matches are:
1. [tex]\(a^2 - 9a + 14 = 0 \quad \longrightarrow \quad \{7, 2\}\)[/tex]
2. [tex]\(a^2 + 9a + 14 = 0 \quad \longrightarrow \quad \{-7, -2\}\)[/tex]
3. [tex]\(a^2 + 3a - 10 = 0 \quad \longrightarrow \quad \{2, -5\}\)[/tex]
4. [tex]\(a^2 + 5a - 14 = 0 \quad \longrightarrow \quad \{2, -4\}\)[/tex]
5. [tex]\(a^2 - 5a - 14 = 0 \quad \longrightarrow \quad \{7, -2\}\)[/tex]
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.
