Monday, November 16, 2015

polynomials - Determine how many roots are real, and finding all roots of a quintic: 2y5+4y42y3y=0

Using a computer we can see that the only real root of f(y)=2y5+4y42y3y=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+4y32y21=0





  • How would we deduce that the remaining roots are not real?

  • How would we find these by hand.

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