Identify the conic section $$$x^{2} + 9 x + 17 = 0$$$

Identify and find the properties of the conic section $$$x^{2} + 9 x + 17 = 0$$$.

The general equation of a conic section is $$$A x^{2} + B x y + C y^{2} + D x + E y + F = 0$$$.

In our case, $$$A = 1$$$, $$$B = 0$$$, $$$C = 0$$$, $$$D = 9$$$, $$$E = 0$$$, $$$F = 17$$$.

The discriminant of the conic section is $$$\Delta = 4 A C F - A E^{2} - B^{2} F + B D E - C D^{2} = 0$$$.

Next, $$$B^{2} - 4 A C = 0$$$.

Since $$$\Delta = 0$$$, this is the degenerated conic section.

Since $$$B^{2} - 4 A C = 0$$$, the equation represents two parallel lines.

$$$x^{2} + 9 x + 17 = 0$$$A represents a pair of the lines $$$x = - \frac{\sqrt{13} + 9}{2}$$$, $$$x = \frac{-9 + \sqrt{13}}{2}$$$A.

General form: $$$x^{2} + 9 x + 17 = 0$$$A.

Factored form: $$$\left(2 x - \sqrt{13} + 9\right) \left(2 x + \sqrt{13} + 9\right) = 0$$$A.

Graph: see the graphing calculator.