Question

find the unique polynomial given the complex roots 1, -1, i, -i, 2 and satisfying the following conditions: f(o)=2, f'(i) not=0, f'(2)=0,f'(1)not=0, f'(-1) not=0, f''(2) not=0, f'(-1) not= 1.

Answer 1

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Answer 2

The idea is if you want f'(a)=0 then (x-a) needs to appears more than one in f(x) (now you can extend this argument to f''). Ok give it a try :)