This question already has an answer here:
Consider the polynomial $( f(x) = x^7 - 4x^3 + x + 1 )$. All the zeroes of the above polynomial are plotted in the complex plane i.e., the Argand plane. How many are within a unit distance from the origin?
Details and Assumptions:
The repeated roots are counted with multiplicity i.e.,$ ( (2x - 1)^2 = 0 )$ has two solutions within a unit distance from origin and not one.
There is a very neat and simple way of doing without W|A. Please refrain from using any such mathematical computational software.