Question Number 55058 by gunawan last updated on 16/Feb/19
$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{P}_{{n}} \left({z}\right)={a}_{\mathrm{0}} {z}^{{n}} +{a}_{\mathrm{1}} {z}^{{n}−\mathrm{1}} +...+{a}_{{n}−\mathrm{1}} {z}+{a}_{{n}} \\ $$$$\mathrm{at}\:\mathrm{least}\:\mathrm{have}\:\mathrm{one}\:\:\mathrm{value}\:\mathrm{of}\:\mathrm{zero} \\ $$