Math CentralQuandaries & Queries


Question from Kumar, a student:

would you please solve this problem, related to complex numbers.

Find all the roots of :

z^5 - 3z^4 + 2z^3 + z^2 - 3z + 2

Hi Kumar,

I can help you get started.

The coefficients in this expression are 1, -3, 2, 1, -3, 2 so taking out a factor of z3 from the first three terms gives

z3(z2 - 3z + 2) + z2 - 3z + 2.

Can you see how to proceed from here? If you get stuck write back and tell us what you did and we will try to help.



No, but I'll give you a hint! Do you see a repeating pattern in the coefficients? (What is 1001 * 314?)

Good Hunting!


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