Answer:
B. [tex]x = \frac{-3 \pm i}{2}[/tex]
Step-by-step explanation:
2x + 6 = -5/x Multiply both sides by x
2x² + 6x = -5 Add 5 to each side
2x² + 6x + 5 = 0
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Apply the quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
a = 2; b = 6; y = 5
[tex]x = \frac{-6\pm\sqrt{6^2-4\times 2 \times 5}}{2\times 2}[/tex]
[tex]x = \frac{-6\pm\sqrt{36-40}}{4}[/tex]
[tex]x = \frac{-6\pm\sqrt{-4}}{4}[/tex]
[tex]x = \frac{-6\pm2i}{4}[/tex]
[tex]x = -\frac{3}{2}\pm\frac{i}{2}[/tex]
[tex]x = \frac{-3 \pm i}{2}[/tex]
The graph of the parabola never reaches the x-axis, so there are no real roots.
