Question

Reconstruct Quartics from roots

score 40 · Answer 1 · 2019-04-07 12:44:59

40

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Reconstruct Quartics from roots

Published on 07 Apr 2019 - 12:44

score 217 · Answer 2 · 2019-04-07 18:58:01

217

Views

Find all values of $a$ for which equation $ e^{x^2} = ax$ always has exactly two roots.

Published on 07 Apr 2019 - 18:58

score 61 · Answer 3 · 2026-03-25 17:19:52

61

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A particular cubic can be written as $y_1^2 = (x_1 - e_1)(x_1 - e_2)(x_1 - e_3)$. Show that $e_1, e_2,$ and $e_3$ are distinct.

Published on 25 Mar 2026 - 17:19

score 597 · Answer 4 · 2026-03-30 00:05:23

597

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Quickest way to find $a^5+b^5+c^5$ given that $a+b+c=1$, $a^2+b^2+c^2=2$ and $a^3+b^3+c^3=3$

Published on 30 Mar 2026 - 0:05

score 66 · Answer 5 · 2026-03-25 12:48:40

66

Views

Find a set of polynomials whose common zero set is $\{(1, 2), (0, 5)\}$.

Published on 25 Mar 2026 - 12:48

score 101 · Answer 6 · 2026-02-23 09:32:39

101

Views

Let $P (x )=x^4+ax^3+bx+c=0$ and have real coefficient and have all real roots . Prove that $ab \leq 0$

Published on 23 Feb 2026 - 9:32

score 27 · Answer 7 · 2019-04-12 17:55:16

27

Views

How can I find the roots of this for k?

Published on 12 Apr 2019 - 17:55

score 72 · Answer 8 · 2026-03-27 10:44:49

72

Views

Roots along a homotopy

Published on 27 Mar 2026 - 10:44

score 128 · Answer 9 · 2019-04-15 06:45:00

128

Views

Number of real roots of $p_n(x)=1+2x+3x^2+....+(n+1)x^n$ if $n$ is an odd integer

Published on 15 Apr 2019 - 6:45

score 447 · Answer 10 · 2026-03-28 01:02:05

447

Views

Quintic polynomial with three real roots

Published on 28 Mar 2026 - 1:02

score 88 · Answer 11 · 2026-03-26 07:59:29

88

Views

Singular points of a matrix when the entries are restriced to a Lie Group

Published on 26 Mar 2026 - 7:59

score 97 · Answer 12 · 2026-03-26 21:09:14

97

Views

Computation of the complex roots of the Laplace transform of a function?

Published on 26 Mar 2026 - 21:09

score 99 · Answer 13 · 2019-04-17 23:10:36

99

Views

Solution to $\sqrt{\sqrt{x + 5} + 5} = x$

Published on 17 Apr 2019 - 23:10

score 261 · Answer 14 · 2019-04-18 16:08:16

261

Views

Finding the eigenvalues of $A=\left(\begin{smallmatrix} a & 1 & 1 \\ 1 & a & 1 \\ 1 & 1 & a \\ \end{smallmatrix}\right)$

Published on 18 Apr 2019 - 16:08

score 428 · Answer 15 · 2019-04-19 03:28:23

428

Views

Continuous function on $[0,1]$ such that its zeros form a nowhere dense set of positive measure?

Published on 19 Apr 2019 - 3:28

List Question

Reconstruct Quartics from roots

Find all values of $a$ for which equation $ e^{x^2} = ax$ always has exactly two roots.

A particular cubic can be written as $y_1^2 = (x_1 - e_1)(x_1 - e_2)(x_1 - e_3)$. Show that $e_1, e_2,$ and $e_3$ are distinct.

Quickest way to find $a^5+b^5+c^5$ given that $a+b+c=1$, $a^2+b^2+c^2=2$ and $a^3+b^3+c^3=3$

Find a set of polynomials whose common zero set is $\{(1, 2), (0, 5)\}$.

Let $P (x )=x^4+ax^3+bx+c=0$ and have real coefficient and have all real roots . Prove that $ab \leq 0$

How can I find the roots of this for k?

Roots along a homotopy

Number of real roots of $p_n(x)=1+2x+3x^2+....+(n+1)x^n$ if $n$ is an odd integer

Quintic polynomial with three real roots

Singular points of a matrix when the entries are restriced to a Lie Group

Computation of the complex roots of the Laplace transform of a function?

Solution to $\sqrt{\sqrt{x + 5} + 5} = x$

Finding the eigenvalues of $A=\left(\begin{smallmatrix} a & 1 & 1 \\ 1 & a & 1 \\ 1 & 1 & a \\ \end{smallmatrix}\right)$

Continuous function on $[0,1]$ such that its zeros form a nowhere dense set of positive measure?

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