Question

What are the roots of `2x + 6 = -(5)/(x)`?
A. `(3stackrel(+)(-) i)/(2)`
B. `(-3stackrel(+)(-) i)/(2)`
C. `(-3stackrel(+)(-) 2i)/(4)`
D. `(3stackrel(+)(-) isqrt(2))/(4)`

Answer 1

Answer:

B. $x = \frac{-3 \pm i}{2}$

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

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

a = 2; b = 6; y = 5

$x = \frac{-6\pm\sqrt{6^2-4\times 2 \times 5}}{2\times 2}$

$x = \frac{-6\pm\sqrt{36-40}}{4}$

$x = \frac{-6\pm\sqrt{-4}}{4}$

$x = \frac{-6\pm2i}{4}$

$x = -\frac{3}{2}\pm\frac{i}{2}$

$x = \frac{-3 \pm i}{2}$

The graph of the parabola never reaches the x-axis, so there are no real roots.