# Tagged Questions

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### Kantorovich Theorem example

I need to write in C a program that finds roots of a 6th order polynomial. I was thinking of using Kantorovich Theorem convergence of Newton's method to find when can I use Newton-Rhapson method. I'm ...
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### Real polynomials, complex zeroes and the Intermediate value theorem

I have a second grad polynomial p(x). For arguments sake lets say $$p(x) = x^2 + 16x + 76$$ I also have an inequation $$p(x) > 0$$ Now the inequation does not have a real solution, but only ...
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### Prove an inequality (Using Taylor expansion)

Prove: $\frac{x}{1+x} < \ln(1+x) < x$. I thought a good practice would be to prove it using Taylor Expansion. Here's my try: $$\ln(1+x) = x - \frac{x^2}{2} + \frac{x^3}{3}...$$ The n=1 ...
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### What is a rational way of factoring polynomials?

Consider the following polynomial $$P_x:=x^4+1$$ I want to represent it as a product of two polynomials with real coefficients of grade $2$. I have done this using, call it, a brute force method. ...
While trying to solve this question my testing lead to an observation that I found interesting in its own right. Consider the linear transformation $L:P\to P$ from the space of polynomial functions ...