How to determine roots of a complex polynomial

65 Views Asked by Bumbble Comm At 25 Apr 2026 - 4:42

Let us consider an equation $x^3+10x^2-100x+1729=0$. Will this equation have at least one complex root having modulus $>12$?

There are 2 best solutions below

Bumbble Comm On 21 Oct 2014 - 8:26

Trying to plot it in an online free tool gave this result enter image description here

I can see that the function crosses x-axis only once around $x = -19.5$, does that help you ?

Bumbble Comm On 21 Oct 2014 - 9:04

enter image description here

This is roots of your equation . As you can see modulus of the complex roots are less that 12 .