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

Match each quadratic equation with its solution set.

[tex]\[
\begin{array}{lll}
2x^2 - 8x + 5 = 0 & 2x^2 - 10x - 3 = 0 & 2x^2 - 8x - 3 = 0 \\
2x^2 - 9x - 1 = 0 & 2x^2 - 9x + 6 = 0 &
\end{array}
\][/tex]

[tex]\[
\begin{array}{l}
\frac{2 \pm \sqrt{80}}{4} \longrightarrow \square \\
\frac{4 \pm \sqrt{22}}{2} \longrightarrow \square
\end{array}
\][/tex]



Answer :

Let's begin by matching each quadratic equation with its solution set.

We use the provided solutions:

1. [tex]\(2x^2 - 8x + 5 = 0\)[/tex]
- Solution: [tex]\[ [2 - \frac{\sqrt{6}}{2}, 2 + \frac{\sqrt{6}}{2}] \][/tex]

2. [tex]\(2x^2 - 10x - 3 = 0\)[/tex]
- Solution: [tex]\[ [\frac{5}{2} - \frac{\sqrt{31}}{2}, \frac{5}{2} + \frac{\sqrt{31}}{2}] \][/tex]

3. [tex]\(2x^2 - 8x - 3 = 0\)[/tex]
- Solution: [tex]\[ [2 - \frac{\sqrt{22}}{2}, 2 + \frac{\sqrt{22}}{2}] \][/tex]

4. [tex]\(2x^2 - 9x - 1 = 0\)[/tex]
- Solution: [tex]\[ [\frac{9}{4} - \frac{\sqrt{89}}{4}, \frac{9}{4} + \frac{\sqrt{89}}{4}] \][/tex]

5. [tex]\(2x^2 - 9x + 6 = 0\)[/tex]
- Solution: [tex]\[ [\frac{9}{4} - \frac{\sqrt{33}}{4}, \frac{9}{4} + \frac{\sqrt{33}}{4}] \][/tex]

Now let's identify the expressions provided:

- [tex]\(\frac{2 \pm \sqrt{80}}{4}\)[/tex]
- Simplification: [tex]\(\frac{2 \pm \sqrt{80}}{4} = \frac{2 \pm \sqrt{4 \cdot 20}}{4} = \frac{2 \pm 2\sqrt{20}}{4} = \frac{2 \pm 2\sqrt{2 \cdot 10}}{4} = \frac{2 \pm 2\sqrt{10}}{4} = \frac{1 \pm \sqrt{10}}{2}\)[/tex]
- None of the equations match with this solution set.

- [tex]\(\frac{4 \pm \sqrt{22}}{2}\)[/tex]
- Simplification: [tex]\(\frac{4 \pm \sqrt{22}}{2} = 2 \pm \frac{\sqrt{22}}{2}\)[/tex]
- This matches with the equation [tex]\(2x^2 - 8x - 3 = 0\)[/tex].

Hence, the correct matches are:

[tex]\[ \begin{array}{l} \frac{2 \pm \sqrt{80}}{4} \longrightarrow \text{None of the provided equations} \\ \frac{4 \pm \sqrt{22}}{2} \longrightarrow 2x^2 - 8x - 3 = 0 \\ \end{array} \][/tex]