Prove-that-P-n-z-a-0-z-n-a-1-z-n-1-a-n-1-z-a-n-at-least-have-one-value-of-zero-

Question Number 55058 by gunawan last updated on 16/Feb/19

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{P}_{{n}} \left({z}\right)={a}_{\mathrm{0}} {z}^{{n}} +{a}_{\mathrm{1}} {z}^{{n}−\mathrm{1}} +…+{a}_{{n}−\mathrm{1}} {z}+{a}_{{n}} \\ $$$$\mathrm{at}\:\mathrm{least}\:\mathrm{have}\:\mathrm{one}\:\:\mathrm{value}\:\mathrm{of}\:\mathrm{zero} \\ $$

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