Let's match each given equation to its respective solution set based on the results.
1. Equation: [tex]\( a^2 - 9a + 14 = 0 \)[/tex]
- Solution Set: [tex]\(\{2, 7\}\)[/tex]
2. Equation: [tex]\( a^2 + 9a + 14 = 0 \)[/tex]
- Solution Set: [tex]\(\{-7, -2\}\)[/tex]
3. Equation: [tex]\( a^2 + 3a - 10 = 0 \)[/tex]
- Solution Set: [tex]\(\{-5, 2\}\)[/tex]
4. Equation: [tex]\( a^2 + 5a - 14 = 0 \)[/tex]
- Solution Set: [tex]\(\{-7, 2\}\)[/tex]
5. Equation: [tex]\( a^2 - 5a - 14 = 0 \)[/tex]
- Solution Set: [tex]\(\{-2, 7\}\)[/tex]
So, the correct pairs are:
- [tex]\( a^2 - 9a + 14 = 0 \)[/tex] → [tex]\(\{2, 7\}\)[/tex]
- [tex]\( a^2 + 9a + 14 = 0 \)[/tex] → [tex]\(\{-7, -2\}\)[/tex]
- [tex]\( a^2 + 3a - 10 = 0 \)[/tex] → [tex]\(\{-5, 2\}\)[/tex]
- [tex]\( a^2 + 5a - 14 = 0 \)[/tex] → [tex]\(\{-7, 2\}\)[/tex]
- [tex]\( a^2 - 5a - 14 = 0 \)[/tex] → [tex]\(\{-2, 7\}\)[/tex]
