Andrew M. answered • 02/13/18

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New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

With a polynomial of degree 15 there are

15 roots. These roots not necessarily distinct,

as with the indicated root of 4 with multiplicity 4

meaning that (x-4)

^{4}is part of the factored p(x).If a nonreal, complex, number a+bi is a root, then

so it's conjugate a-bi

The roots we have accounted for are thus:

1-i, 1+i, -3i, 3i, 4 with multiplicity 4...

This is 8 of 15 roots leaving 7 unaccounted for.

Maximum number real zeroes = 11 since we

know there are at least 4 nonreal zeroes.

Maximum number of nonreal zeroes:

We have 4 real zeroes identified leaving

11 possible zeroes. . As discussed,

nonreal zeroes come in pairs and the total

zeroes is 15... Maximum number of nonreal

zeroes is 10 in 5 sets of complex conjugate pairs.

Note that 4 of those 10 are already identified.