Given: $x^{-2} + 2x^{-1} - 15 = 0$

Rewrite as: $\frac{1}{x^2} + \frac{2}{x} - 15 = 0$

Eliminate fractions by multiplying both sides by $x^2$ to get: $1 + 2x - 15x^2 = 0$

Rearrange to get: $15x^2 - 2x - 1 = 0$

Factor to get: $(5x + 1)(3x - 1) = 0$

So, EITHER $5x + 1 = 0$ OR $3x - 1 = 0$

If $5x + 1 = 0$, then $x = -\frac{1}{5}$

If $3x - 1 = 0$, then $x = \frac{1}{3}$

So, the roots (solutions) are $-\frac{1}{5}$ and $\frac{1}{3}$

Answer: B