not sure what techniques you have to use. You can use Descartes' Rule of Signs, or the signs produced in synthetic division to get a handle on the bounds, but otherwise you may be stuck with iterative numeric techniques.
If you have calculus under your belt, then we can check for extrema and concavity:
y = -x^4+2x^2+x-4
y' = -4x^3+4x+1
y" = -12x^2+4
Now we're not much better off. The derivatives also have no rational zeros. You can check y' and find that it is zero at x = -.837, -.269, 1.107
at hose values of x, y= -3.93, -4.13, -1.94
also, y" is negative, positive, negative
That means that we have a global maximum at x=1.107, and y is negative there, so there are no possible roots for y.
approximate all zeros and extrema to the nearest hundredth. how many zeros, if any, are imaginary.
-x^4+2x^2+x-4.
Are there no zeros?
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