Using a computer we can see that the only real root of f(y)=−2y5+4y4−2y3−y=0 is 0. Furthermore, we know from algebra that since this polynomial lives in R[y] that the roots come in complex conjugate pairs. I.e. we knew that there were either 1,3 or 5 real roots of this polynomial. Furthermore, if we could guess factors, we could complete polynomial long division to break up the polynomial. Noting that y=0 is a root, we want the 4 roots of:
−2y4+4y3−2y2−1=0
- How would we deduce that the remaining roots are not real?
- How would we find these by hand.
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