Question 491587
Looking at the graph is often helpful:
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{{{graph(500,500,-10,10,-30,30,x^4-8*x^2-9)}}}
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This shows the x-intercepts to be:  (-3,0) and (3,0).
This shows the y-intercept to be:  (0,-9).
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You also can look this another way using the following substitution:
{{{u = x^2}}}
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{{{y = u^2 -8u - 9}}}
{{{y = (u +1)(u-9)}}}
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{{{y = (x^2+1)*(x^2-9)}}}
{{{y = (x^2+1) * (x-3)(x+3)}}}
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Clearly, two of the roots are
{{{x = 3}}}
{{{x = -3}}}
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But factoring x^2+1 is a problem because to have to solve
{{{x^2 + 1 = 0}}}
In turn, that means:
{{{x^2 = -1}}}
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Of course, that defines an imaginary number.
{{{i^2 = -1}}}
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Looking back at the original equation:
{{{y = x^4 -8x^2 -9}}}
We can tell by inspection that when x=0, y = -9.
That defines the point (0,-9).
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So, perhaps the book has an error.
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Done.