Answer:
(See explanation for further details)
Step-by-step explanation:
The real expression is:
[tex](k^{2}-1)\cdot x{{2} - 2\cdot k \cdot x - 3\cdot k + 1 = 0[/tex]
The general equation for the second-order polynomial is:
[tex]x = \frac{2\cdot k \pm \sqrt{4\cdot k^{2}-4\cdot (k^{2}-1)\cdot (-3\cdot k + 1)}}{k^{2}-1}[/tex]
This condition must be observed for the case of a quadratic equation with equal roots:
[tex]4\cdot k^{2} - 4\cdot (k^{2}-1)\cdot (-3\cdot k + 1) = 0[/tex]
[tex]k^{2} + (k^{2}-1)\cdot (3\cdot k + 1) = 0[/tex]
[tex]k^{2} + 3\cdot k^{3} - 3\cdot k - k^{2}-1 = 0[/tex]
[tex]3\cdot k^{3} - 3\cdot k - 1 = 0[/tex]
