martinezadam576
Answered

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Match each equation with its solution set.

[tex]\[
\begin{array}{lll}
a^2-9a+14=0 & a^2+9a+14=0 & a^2+3a-10=0 \\
a^2-5a-14=0 & a^2+5a-14=0
\end{array}
\][/tex]

[tex]\[
\{-2, 7\} \longrightarrow \square
\][/tex]

[tex]\[
\{2, -7\} \longrightarrow \square
\][/tex]

[tex]\[
\{7, 2\} \longrightarrow \square
\][/tex]

Sagot :

GinnyAnswer
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].
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