Question

Challenge Question!

Let \(f(z)\) be the polynomial\[f(z)=2z^5-6z^2+z+1\] over the complex numbers \(\mathbb{C}\). How many roots does \(f\) have in the region\[1<|z|<2=\{x+iy\in\mathbb{C}\,|\,1<\sqrt{x^2+y^2}<2\}?\]

Answer 1

How would one start this question? Its like alien language to me.

Answer 2

There's a reason it's a challenge question :)

Answer 3

Good point.

Answer 4

ive been trying to solve this and i cant get the answer ;-;