1. The problem statement, all variables and given/known data Let a0 > a1 > a2 > ... > an > 0 be coefficients of a polynomial P(z) = a0 + a1z + a2z2 + ... + anzn. Let z0 be complex number such that P(z0) = 0. Show that |z0| > 1. 2. Relevant equations Triangle inequality? Not sure if that's enough. 3. The attempt at a solution I started with asumption that P(z0) = 0 with some |z0| < 1. Then I made a pair of equations: z0P(z0) = 0 P(z0) = 0 Subtraction gives a new equation z0P(z0) - P(z0) = 0 I rearranged the terms -a0 + (a0 - a1)z0 + ... + (an-1 - an)z0n + anz0n+1 = 0 and took a modulus of it. Then by using triangle inequality (and the asumption that |z0| < 1) I got a contradiction 0 > 0. So the modulus of z0 must be greater or equal to 1. For the second part of the task, I also tried a similar approach (assumed that |z0| = 1 and tried to make it lead to a contradiction) but couldn't get anything out of it. In the first part I needed the asumption that |z0| < 1 to get the contradiction 0 < 0. Now the same approach leads to inequality 0 [tex]\leq[/tex] 0 which is true. Any tips?