Answer :
Let's match each quadratic equation to its corresponding solution set:
1. For the quadratic equation [tex]\(2x^2 - 8x + 5 = 0\)[/tex], the solutions are:
[tex]\[ \left(2 - \frac{\sqrt{6}}{2}, 2 + \frac{\sqrt{6}}{2}\right) \][/tex]
2. For the quadratic equation [tex]\(2x^2 - 10x - 3 = 0\)[/tex], the solutions are:
[tex]\[ \left(\frac{5}{2} - \frac{\sqrt{31}}{2}, \frac{5}{2} + \frac{\sqrt{31}}{2}\right) \][/tex]
3. For the quadratic equation [tex]\(2x^2 - 8x - 3 = 0\)[/tex], the solutions are:
[tex]\[ \left(2 - \frac{\sqrt{22}}{2}, 2 + \frac{\sqrt{22}}{2}\right) \][/tex]
4. For the quadratic equation [tex]\(2x^2 - 9x - 1 = 0\)[/tex], the solutions are:
[tex]\[ \left(\frac{9}{4} - \frac{\sqrt{89}}{4}, \frac{9}{4} + \frac{\sqrt{89}}{4}\right) \][/tex]
5. For the quadratic equation [tex]\(2x^2 - 9x + 6 = 0\)[/tex], the solutions are:
[tex]\[ \left(\frac{9}{4} - \frac{\sqrt{33}}{4}, \frac{9}{4} + \frac{\sqrt{33}}{4}\right) \][/tex]
Matching the equations with their solutions:
- [tex]\(2x^2 - 8x + 5 = 0\)[/tex] matches [tex]\(\left(2 - \frac{\sqrt{6}}{2}, 2 + \frac{\sqrt{6}}{2}\right)\)[/tex]
- [tex]\(2x^2 - 10x - 3 = 0\)[/tex] matches [tex]\(\left(\frac{5}{2} - \frac{\sqrt{31}}{2}, \frac{5}{2} + \frac{\sqrt{31}}{2}\right)\)[/tex]
- [tex]\(2x^2 - 8x - 3 = 0\)[/tex] matches [tex]\(\left(2 - \frac{\sqrt{22}}{2}, 2 + \frac{\sqrt{22}}{2}\right)\)[/tex]
- [tex]\(2x^2 - 9x - 1 = 0\)[/tex] matches [tex]\(\left(\frac{9}{4} - \frac{\sqrt{89}}{4}, \frac{9}{4} + \frac{\sqrt{89}}{4}\right)\)[/tex]
- [tex]\(2x^2 - 9x + 6 = 0\)[/tex] matches [tex]\(\left(\frac{9}{4} - \frac{\sqrt{33}}{4}, \frac{\sqrt{33}}{4} + \frac{9}{4}\right)\)[/tex]
Thus, the pairs are:
1. [tex]\(2x^2 - 8x + 5 = 0\)[/tex] and [tex]\(\left(2 - \frac{\sqrt{6}}{2}, 2 + \frac{\sqrt{6}}{2}\right)\)[/tex]
2. [tex]\(2x^2 - 10x - 3 = 0\)[/tex] and [tex]\(\left(\frac{5}{2} - \frac{\sqrt{31}}{2}, \frac{5}{2} + \frac{\sqrt{31}}{2}\right)\)[/tex]
3. [tex]\(2x^2 - 8x - 3 = 0\)[/tex] and [tex]\(\left(2 - \frac{\sqrt{22}}{2}, 2 + \frac{\sqrt{22}}{2}\right)\)[/tex]
4. [tex]\(2x^2 - 9x - 1 = 0\)[/tex] and [tex]\(\left(\frac{9}{4} - \frac{\sqrt{89}}{4}, \frac{9}{4} + \frac{\sqrt{89}}{4}\right)\)[/tex]
5. [tex]\(2x^2 - 9x + 6 = 0\)[/tex] and [tex]\(\left(\frac{9}{4} - \frac{\sqrt{33}}{4}, \frac{9}{4} + \frac{\sqrt{33}}{4}\right)\)[/tex]
By dragging the corresponding solutions to their equations, you will correctly complete the match.
1. For the quadratic equation [tex]\(2x^2 - 8x + 5 = 0\)[/tex], the solutions are:
[tex]\[ \left(2 - \frac{\sqrt{6}}{2}, 2 + \frac{\sqrt{6}}{2}\right) \][/tex]
2. For the quadratic equation [tex]\(2x^2 - 10x - 3 = 0\)[/tex], the solutions are:
[tex]\[ \left(\frac{5}{2} - \frac{\sqrt{31}}{2}, \frac{5}{2} + \frac{\sqrt{31}}{2}\right) \][/tex]
3. For the quadratic equation [tex]\(2x^2 - 8x - 3 = 0\)[/tex], the solutions are:
[tex]\[ \left(2 - \frac{\sqrt{22}}{2}, 2 + \frac{\sqrt{22}}{2}\right) \][/tex]
4. For the quadratic equation [tex]\(2x^2 - 9x - 1 = 0\)[/tex], the solutions are:
[tex]\[ \left(\frac{9}{4} - \frac{\sqrt{89}}{4}, \frac{9}{4} + \frac{\sqrt{89}}{4}\right) \][/tex]
5. For the quadratic equation [tex]\(2x^2 - 9x + 6 = 0\)[/tex], the solutions are:
[tex]\[ \left(\frac{9}{4} - \frac{\sqrt{33}}{4}, \frac{9}{4} + \frac{\sqrt{33}}{4}\right) \][/tex]
Matching the equations with their solutions:
- [tex]\(2x^2 - 8x + 5 = 0\)[/tex] matches [tex]\(\left(2 - \frac{\sqrt{6}}{2}, 2 + \frac{\sqrt{6}}{2}\right)\)[/tex]
- [tex]\(2x^2 - 10x - 3 = 0\)[/tex] matches [tex]\(\left(\frac{5}{2} - \frac{\sqrt{31}}{2}, \frac{5}{2} + \frac{\sqrt{31}}{2}\right)\)[/tex]
- [tex]\(2x^2 - 8x - 3 = 0\)[/tex] matches [tex]\(\left(2 - \frac{\sqrt{22}}{2}, 2 + \frac{\sqrt{22}}{2}\right)\)[/tex]
- [tex]\(2x^2 - 9x - 1 = 0\)[/tex] matches [tex]\(\left(\frac{9}{4} - \frac{\sqrt{89}}{4}, \frac{9}{4} + \frac{\sqrt{89}}{4}\right)\)[/tex]
- [tex]\(2x^2 - 9x + 6 = 0\)[/tex] matches [tex]\(\left(\frac{9}{4} - \frac{\sqrt{33}}{4}, \frac{\sqrt{33}}{4} + \frac{9}{4}\right)\)[/tex]
Thus, the pairs are:
1. [tex]\(2x^2 - 8x + 5 = 0\)[/tex] and [tex]\(\left(2 - \frac{\sqrt{6}}{2}, 2 + \frac{\sqrt{6}}{2}\right)\)[/tex]
2. [tex]\(2x^2 - 10x - 3 = 0\)[/tex] and [tex]\(\left(\frac{5}{2} - \frac{\sqrt{31}}{2}, \frac{5}{2} + \frac{\sqrt{31}}{2}\right)\)[/tex]
3. [tex]\(2x^2 - 8x - 3 = 0\)[/tex] and [tex]\(\left(2 - \frac{\sqrt{22}}{2}, 2 + \frac{\sqrt{22}}{2}\right)\)[/tex]
4. [tex]\(2x^2 - 9x - 1 = 0\)[/tex] and [tex]\(\left(\frac{9}{4} - \frac{\sqrt{89}}{4}, \frac{9}{4} + \frac{\sqrt{89}}{4}\right)\)[/tex]
5. [tex]\(2x^2 - 9x + 6 = 0\)[/tex] and [tex]\(\left(\frac{9}{4} - \frac{\sqrt{33}}{4}, \frac{9}{4} + \frac{\sqrt{33}}{4}\right)\)[/tex]
By dragging the corresponding solutions to their equations, you will correctly complete the match.
