Question

Can the solution to $x^4+\frac{13}6Ux^3+\frac32U^2x^2+\frac13U^3x-V=0$ be written as a sum of quartic roots?

score 137 · Answer 1 · 2023-07-11 15:03:59

137

Views

Can the solution to $x^4+\frac{13}6Ux^3+\frac32U^2x^2+\frac13U^3x-V=0$ be written as a sum of quartic roots?

Published on 11 Jul 2023 - 15:03

score 55 · Answer 2 · 2026-02-23 06:36:11

55

Views

Root representation using the factorization of polynomials upto degree six

Published on 23 Feb 2026 - 6:36

score 29 · Answer 3 · 2023-08-22 23:01:32

29

Views

Efficient representations of the angular dependence of quadratic and quartic functions in 2d

Published on 22 Aug 2023 - 23:01

score 41 · Answer 4 · 2023-09-05 03:21:07

41

Views

How to find smallest positive real roots of $\left(At^2+Bt+C\right)\left(Dt^2+Gt+H\right)-k^2=0$ given $A,B,C,D,G,H\in C$ and $k\in R$?

Published on 05 Sep 2023 - 3:21

score 80 · Answer 5 · 2023-09-14 16:43:27

80

Views

Find quartic equation combining equation of ellipse and circle

Published on 14 Sep 2023 - 16:43

score 191 · Answer 6 · 2023-09-22 05:43:34

191

Views

What must be true for thirteen points to impose independent conditions on quartics?

Published on 22 Sep 2023 - 5:43

score 204 · Answer 7 · 2023-10-17 03:51:48

204

Views

The relation between the number of solution of $f(x)=x$ and $f(f(x))=x$, when f is a quartic polynomial

Published on 17 Oct 2023 - 3:51

score 89 · Answer 8 · 2023-10-18 18:28:23

89

Views

Show that the roots of the equation $b^2(x^4+1)-14b(1+b^2)x(x^2+1)+(1+196b^2+b^4)x^2=0$ are all real and all have the same sign as $b$.

Published on 18 Oct 2023 - 18:28

score 112 · Answer 9 · 2023-10-18 20:53:24

112

Views

Find $\sin{\frac{\pi}{10}}$ in form of $a+b\sqrt{k}$

Published on 18 Oct 2023 - 20:53

score 46 · Answer 10 · 2023-10-26 13:46:28

46

Views

Coefficient of a quartic polynomial given the conditions it's a natural number and has atleast one real root

Published on 26 Oct 2023 - 13:46

score 42 · Answer 11 · 2023-10-26 15:33:12

42

Views

Erratum in Boyd and Vanderberghe p. 30?

Published on 26 Oct 2023 - 15:33

score 88 · Answer 12 · 2023-11-01 21:42:50

88

Views

How many roots in a system of quartic equations

Published on 01 Nov 2023 - 21:42

score 171 · Answer 13 · 2026-03-22 05:05:21

171

Views

Invariants of a quartic function

Published on 22 Mar 2026 - 5:05

score 278 · Answer 14 · 2023-12-02 13:29:03

278

Views

Solve equation $(3x^2-2x-1)^2-(6x^2-4x-5)^2+x=0$

Published on 02 Dec 2023 - 13:29

score 199 · Answer 15 · 2023-12-13 22:37:05

199

Views

Star number equals product of consecutive star numbers

Published on 13 Dec 2023 - 22:37

List Question

Can the solution to $x^4+\frac{13}6Ux^3+\frac32U^2x^2+\frac13U^3x-V=0$ be written as a sum of quartic roots?

Root representation using the factorization of polynomials upto degree six

Efficient representations of the angular dependence of quadratic and quartic functions in 2d

How to find smallest positive real roots of $\left(At^2+Bt+C\right)\left(Dt^2+Gt+H\right)-k^2=0$ given $A,B,C,D,G,H\in C$ and $k\in R$?

Find quartic equation combining equation of ellipse and circle

What must be true for thirteen points to impose independent conditions on quartics?

The relation between the number of solution of $f(x)=x$ and $f(f(x))=x$, when f is a quartic polynomial

Show that the roots of the equation $b^2(x^4+1)-14b(1+b^2)x(x^2+1)+(1+196b^2+b^4)x^2=0$ are all real and all have the same sign as $b$.

Find $\sin{\frac{\pi}{10}}$ in form of $a+b\sqrt{k}$

Coefficient of a quartic polynomial given the conditions it's a natural number and has atleast one real root

Erratum in Boyd and Vanderberghe p. 30?

How many roots in a system of quartic equations

Invariants of a quartic function

Solve equation $(3x^2-2x-1)^2-(6x^2-4x-5)^2+x=0$

Star number equals product of consecutive star numbers

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