Find x- and y- Intercepts....3

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mathdad
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Find the x- and y-intercepts.

y = 8x^3 - 6x - 1

Let x = 0

y = 8(0)^3 - 6(0) - 1

y = -1

The y-intercept is y = -1 and it takes place at the point
(0, -1).

To find the x-intercept, let y = 0.

0 = 8x^3 - 6x - 1

I am stuck here.
 
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I don't think this one has "nice" roots. :(
 
What do "nice" roots look like?