Question

Showing $P_{n+1}(x)=x^2(P_n(x)-\frac{\mathrm d}{\mathrm dx}P_n(x))$ where $P_n$ is a polynomial of degree $n$

score 78 · Answer 1 · 2018-04-25 11:34:23

78

Views

Showing $P_{n+1}(x)=x^2(P_n(x)-\frac{\mathrm d}{\mathrm dx}P_n(x))$ where $P_n$ is a polynomial of degree $n$

Published on 25 Apr 2018 - 11:34

score 500 · Answer 2 · 2026-03-30 02:30:53

500

Views

How can the turning point on the graph be estimated

Published on 30 Mar 2026 - 2:30

score 61 · Answer 3 · 2026-03-25 04:39:28

61

Views

Polynomial question: find $a$ such that all roots are real.

Published on 25 Mar 2026 - 4:39

score 95 · Answer 4 · 2026-03-30 03:24:58

95

Views

Finite polynomial maps

Published on 30 Mar 2026 - 3:24

score 70 · Answer 5 · 2018-04-25 18:23:22

70

Views

Find the limit of some roots raised to n

Published on 25 Apr 2018 - 18:23

score 311 · Answer 6 · 2026-03-25 06:29:32

311

Views

Is polynomial $x^{2n-1}-4nx^{2n-2}-2\binom{2n}{3}x^{2n-4}-\dots-2\binom{2n}{3}x^{2}-4n$ irreducible?

Published on 25 Mar 2026 - 6:29

score 268 · Answer 7 · 2026-03-28 09:51:21

268

Views

Let $f \in \mathbb{Z}[x]$. Is the number of roots of $\bar{f}$ in $\bar{\mathbb{F}_p}$ bounded above by the number of roots of of $f$ in $\mathbb{C}$?

Published on 28 Mar 2026 - 9:51

score 1.3k · Answer 8 · 2026-03-25 12:28:09

1.3k

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If $x+1$ is a factor of $ax^4 + bx^2 + c,$ what is the value of $a + b + c?$

Published on 25 Mar 2026 - 12:28

score 83 · Answer 9 · 2018-04-26 07:24:49

83

Views

A nontrivial solution to polynomial $k[x_1,\ldots, x_n ]$

Published on 26 Apr 2018 - 7:24

score 87 · Answer 10 · 2026-03-26 08:02:37

87

Views

Understanding the position in the complex plane of the roots of a polynomial of degree three

Published on 26 Mar 2026 - 8:02

score 84 · Answer 11 · 2018-04-26 08:17:30

If $x_0$ is a real root of $p(x)=x^4+a_3 x^3 + a_2 x^2 +a_1 x + a_0$ and $p'(x_0) \ne 0$. Does $p(x)$ have at least two real roots?

score 111 · Answer 12 · 2026-03-28 21:26:53

111

Views

Why does the polynomial $x^{n+1}-n!$ have $n+1$ distinct roots?

Published on 28 Mar 2026 - 21:26

score 98 · Answer 13 · 2018-04-26 10:51:38

98

Views

How good are these probabilistic algorithms for the NP-hard problem gcd of sparse polynomials?

Published on 26 Apr 2018 - 10:51

score 58 · Answer 14 · 2018-04-26 14:00:59

58

Views

How can I find the root of this polynomial?

Published on 26 Apr 2018 - 14:00

score 87 · Answer 15 · 2026-03-29 10:09:40

87

Views

Linear transformation given by matrix multiplication

Published on 29 Mar 2026 - 10:09

List Question

Showing $P_{n+1}(x)=x^2(P_n(x)-\frac{\mathrm d}{\mathrm dx}P_n(x))$ where $P_n$ is a polynomial of degree $n$

How can the turning point on the graph be estimated

Polynomial question: find $a$ such that all roots are real.

Finite polynomial maps

Find the limit of some roots raised to n

Is polynomial $x^{2n-1}-4nx^{2n-2}-2\binom{2n}{3}x^{2n-4}-\dots-2\binom{2n}{3}x^{2}-4n$ irreducible?

Let $f \in \mathbb{Z}[x]$. Is the number of roots of $\bar{f}$ in $\bar{\mathbb{F}_p}$ bounded above by the number of roots of of $f$ in $\mathbb{C}$?

If $x+1$ is a factor of $ax^4 + bx^2 + c,$ what is the value of $a + b + c?$

A nontrivial solution to polynomial $k[x_1,\ldots, x_n ]$

Understanding the position in the complex plane of the roots of a polynomial of degree three

If $x_0$ is a real root of $p(x)=x^4+a_3 x^3 + a_2 x^2 +a_1 x + a_0$ and $p'(x_0) \ne 0$. Does $p(x)$ have at least two real roots?

Why does the polynomial $x^{n+1}-n!$ have $n+1$ distinct roots?

How good are these probabilistic algorithms for the NP-hard problem gcd of sparse polynomials?

How can I find the root of this polynomial?

Linear transformation given by matrix multiplication

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