Tagged Questions

53 views

no positive roots for $(y+1)^{7}-2(y+1)^{5}+10(y+1)^{2}-1$

Hint for showing that $(y+1)^{7}-2(y+1)^{5}+10(y+1)^{2}-1$ has no positive roots thanks
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100th degree polynomial $P(2^k)=k$ for $k=0,1,…100$

I sometimes see this kind of question, but I completely forgot how to solve it. Could anyone solve it for me?
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Approximations other than taylor series and pade approximation

I have a function which has the following form: $$f(x)=K_1 \coth (Q_1 Q_2 \sqrt{x})^2 + \frac{1}{x}\left[K_2 + K_3 \coth(Q_1 Q_3\sqrt{x})\sqrt{x}\right]$$ and I want to find $x$ for $f(x)=1$. I'm ...
54 views

Non-linear system of 4 unknowns

What are the non-zero solutions in $x,y,z$ and $t$ of the following system of equations \begin{cases} (1+ax+bz)(1-x)=1\\ (1+cy+bt)(1-y)=1 \\ (1+dx+bt)(1-z)=1\\ (1+fy+bz)(1-t)=1 \end{cases}
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Solving for $f(n+1)$ when $f(k)$ is known for $k=0,1,…,n$

I posted earlier about polynomials but this is different type of problem I think. I seem to have an answer but I mistrust it.... A polynomial $f(x)$ where deg[$f(x)$]$\le{n}$ satisfies $f(k)=2^k$ ...
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system of equations with three equations.

We have to find all real solutions to this system of equations: $$x=\frac{4z^2}{1+4z^2},y=\frac{4x^2}{1+4x^2},z=\frac{4y^2}{1+4y^2}$$
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Find all polynomials that fix $\mathbb Q$ and the irrationals

Problem: Describe all polynomials $\mathbb{R}\rightarrow\mathbb{R}$ with coefficients in $\mathbb C$ which send rational numbers to rational numbers and irrational numbers to irrational numbers.
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Finding roots of product of two polynomials

Let $P$ and $Q$ be polynomials of degree $2$ and $3$ respectively. If we know the roots of both $P$ and $Q$, is there an easier way of finding the roots of the product $PQ$? Do we really have to ...
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simple arithmetic problem but..

i am having problem in this proof. i need to find the certain coefficients of this statement on the right side. given: $P: \mathbb{C} \Longrightarrow \mathbb{C}, \quad P(x) := 12 − 7x + x^2$ \$Q : ...
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Which polynomial equations of higher degree will have a solution formula?

A polynomial equation of degree greater than four will in general have no solution formula. But what are some typical cases one should be aware of as a practical person in which there are solutions?