Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Match each equation with its solution set.
[tex]\[
\begin{array}{l}
a^2 - 9a + 14 = 0 \quad \{2, 7\} \\
a^2 + 9a + 14 = 0 \quad \{-2, -7\} \\
a^2 + 3a - 10 = 0 \quad \{-5, 2\} \\
a^2 + 5a - 14 = 0 \quad \{-7, 2\} \\
a^2 - 5a - 14 = 0 \quad \{7, -2\} \\
\end{array}
\][/tex]


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]