Sure, let's pair each quadratic equation with its solution set based on their roots. Here are the correct pairs:
1. For the equation [tex]\( a^2 - 9a + 14 = 0 \)[/tex]:
- The solutions are [tex]\( a = 2 \)[/tex] and [tex]\( a = 7 \)[/tex].
- So, the solution set is [tex]\(\{2, 7\}\)[/tex].
- Using a different notation, it can be written as [tex]\(\{7, 2\}\)[/tex].
2. For the equation [tex]\( a^2 + 9a + 14 = 0 \)[/tex]:
- The solutions are [tex]\( a = -7 \)[/tex] and [tex]\( a = -2 \)[/tex].
- So, the solution set is [tex]\(\{-7, -2\}\)[/tex].
3. For the equation [tex]\( a^2 + 3a - 10 = 0 \)[/tex]:
- The solutions are [tex]\( a = -5 \)[/tex] and [tex]\( a = 2 \)[/tex].
- So, the solution set is [tex]\(\{-5, 2\}\)[/tex].
4. For the equation [tex]\( a^2 - 5a - 14 = 0 \)[/tex]:
- The solutions are [tex]\( a = 7 \)[/tex] and [tex]\( a = -2 \)[/tex].
- So, the solution set is [tex]\(\{7, -2\}\)[/tex].
5. For the equation [tex]\( a^2 + 5a - 14 = 0 \)[/tex]:
- The solutions are [tex]\( a = -7 \)[/tex] and [tex]\( a = 2 \)[/tex].
- So, the solution set is [tex]\(\{-7, 2\}\)[/tex].
Given these, the correct matches are:
- [tex]\( \{7, 2\} \)[/tex] matches with [tex]\( a^2 - 5a - 14 = 0 \)[/tex].
- The other solution sets can be:
- [tex]\( \{-2, 7\} \)[/tex] matches with [tex]\( a^2 - 9a + 14 = 0 \)[/tex].
- [tex]\(\{2, -7\}\)[/tex] matches with [tex]\( a^2 + 5a - 14 = 0 \)[/tex].
Putting these altogether, the final pairs would be:
- [tex]\( \{2, -7\} \longrightarrow a^2 + 5a - 14 = 0 \)[/tex]
- [tex]\( \{7, 2\} \longrightarrow a^2 - 5a - 14 = 0 \)[/tex]
- [tex]\( \{-2, 7\} \longrightarrow a^2 - 9a + 14 = 0 \)[/tex].
