# Tagged Questions

This tag is used for both basic and advanced questions on polynomials in any number of variables. Including, but not limited to: solving for roots, factoring, checking for irreducibility. This tag is rarely used as the only tag for a question.

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### Undefined derivative of a third degree polynomial inverse?

I have the following equation: $$r_t=kr_s^{3}+r_s$$ I need to get $r_s'$, i.e. derivative of $r_s$ w.r.t. $k$, provided that value of $r_t'$ is already known. Taking derivatives of both sides w.r.t. ...
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### For which polynomials $f$ is the subset {$f(x):x∈ℤ$} of $ℤ$ closed under multiplication?

You surely know about the Brahmagupta–Fibonacci identity, $$(a_1^2 + b_1^2)(a_2^2 + b_2^2) = (a_1a_2 \pm b_1b_2)^2 + (a_1b_2 \mp a_2b_1)^2$$ which tells us that the product of two numbers, each of ...
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### A question on roots of a polynomial of degree $n$

Under what conditions on cofficients of a polynomial $p(x)$, the roots of $p(x)$ are real and positive?
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### Polynomials equations

I am trying to find the common solutions of this equations: $$2x^4+x^3-5x^2+2x=0$$ $$2(2x-1)^{1998}+(4x-1)^{1997}=4x+1$$. My idea is to solve the first one. I find the solutions:$x=1$ , $x=0$ , ...
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### What does $\mathbb{Z}[X]$ for a polynom mean?

I have a proof saying that a Polynom $p \in \mathbb{Z}[X_1,...,X_m]$ I'm a bit confused of this notation because neither X nor the m is explains somewhere. Does somebody of you know the notation?
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### Find the value of $k$ in the equation [closed]

Find the value of $k$ for which the equation $$kx^2-2015x+(k-2015)=0$$ has one positive and one negative root.
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### Find the perfect square trinomial! [closed]

Fill in the blank to complete the perfect square trinomial: $$z^8+\_\_\_+144$$
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### Finding the range of a $y=-x^2(x+5)(x-3)$ without calculus?

I was helping a precalculus student with this question. The graph wasn't given. My only idea was to find the inverse and try to find its domain. When trying to find the inverse, I arrived at ...
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### Why $|x|$ is not rational expression?

I'm 9th grade student, and my teacher said that $|x|$ is not rational expression ( expression like $\frac{p(x)}{q(x)}$ s.t $p(x)$ and $q(x)\neq 0$ are polynomial) but he didn't have convincing reason. ...
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Short version of the question: Guess the next terms in the sequence : $D_{17},D_{19},D_{23}$ etc where $$\begin{array}{lcl} D_3 &=& (a\pm 1) \\ D_5 &=& (a\pm 1) (a^2-1 \pm 11a) \\ ... 1answer 32 views ### solution of system of polynomials I have 3 equations as following:$$ \left\{ \begin{array}{c} (\Delta_{11}*y^2 + \Delta_{12}*y + \Delta_{13})x^2 + (\Delta_{21}*y^2 + \Delta_{22}*y + \Delta_{23})x + \Delta_{31}*y^2 + \Delta_{32}*y + ...
I'm asked to compute the Jacobian of a system of equations $x_1^4+x_2^4-1=0$ $x_2-\sin(5x_1)=0$ $x_1-x_3^2=0$ What's the Jacobian of a system of equations? Do I perhaps need to infer the individual ...