## Application of Newton-Raphson: OMO Spring 2018

This year’s OMO included this problem: 13. Find the smallest positive integer for which the polynomial has a real root greater than 1.999. Solution. Equivalently, the polynomial is if is […]

Because it is fairly complicated, Sturm’s Theorem is best taught with an example. In the last post, we were investigating the roots of the function via Newton’s method, and we […]

Say you’re in a competition and you need to calculate the square root of two to several decimal places. Or perhaps you need to approximate the roots to an unwieldy […]

Problem 1: Find the sum of the coefficients of the even-power terms of the polynomial given that and To solve this problem, let’s write down a simple example: Now lets plug […]