Let `u=x^-1`. Then we have:

`10u^2+3u-1=0`

` (5u-1)(2u+1)=0`

So `u=1/5 or -1/2`

This gives us `x^-1=1/5` so `x = 5`

and `x^-1=-1/2` so `x=-2`.

Always CHECK your answers!!

Here's the graph of the function, to help clarify the situation. This time we sketch `y = 10x^-2 + 3x^-1 -1`.

12345678910-1-2-3-4-51020xyOpen image in a new page

Graph of `y = 10x^-2 + 3x^-1 -1`

The two intersections with the x-axis are at `x = -2` and `x=5`.

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