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Say I have a fifth degree polynomial $$z^5-5z^4-188z^3+986z^2+10152z-59696$$ with the roots $$ 7, 9-i,9 + i,-10 + 2i,-10 - 2i.$$ Say I want a sixth degree polynomial instead with the same roots. Can that be done?

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Doesntusefacebook
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    Multiply the 5th degree polynomial by $(z-7)$ or $(z-9+I)$ or ... – Oleg567 Oct 04 '18 at 13:48
  • what about multiplying by $z$? – Pavel R. Oct 04 '18 at 13:49
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    @Pavel R.: then $6$th root will be $0$ (but given task is "...with the same roots"). – Oleg567 Oct 04 '18 at 13:50
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    @Oleg567: $(x-7)$ is the only possible multiplicand if you want the resulting polynomial to have integer coefficients (which is probably what the OP wants, although they don't say so explicitly). – TonyK Oct 04 '18 at 14:06
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    @Doesntusefacebook: Please edit your Question to confirm that you would allow your sixth degree polynomial to repeat a root of the given fifth degree polynomial, and clarify if you require the resulting polynomial to have integer coefficients. – hardmath Oct 04 '18 at 14:35

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