Question

Quartic with only one singular point

score 97 · Answer 1 · 2022-07-20 14:40:08

97

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Quartic with only one singular point

Published on 20 Jul 2022 - 14:40

score 51 · Answer 2 · 2022-07-28 17:27:54

51

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Resting a stick in a cup. How far away from the side will it be?

Published on 28 Jul 2022 - 17:27

score 52 · Answer 3 · 2022-07-31 13:03:42

52

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Square roots of root-expressions: distinguishing quartic Galois groups from copies of $C_4$ or of $D_4$ - exercise M.11, Ch.16 Artin's algebra

Published on 31 Jul 2022 - 13:03

score 351 · Answer 4 · 2022-08-03 15:29:53

351

Views

Prove $f(-\frac12) \le \frac{3}{16}$ if all roots of $f(x) = x^4 - x^3 + a x + b$ are real

Published on 03 Aug 2022 - 15:29

score 112 · Answer 5 · 2022-08-14 20:29:44

112

Views

is there a cubic or quartic approximation for these data points?

Published on 14 Aug 2022 - 20:29

score 147 · Answer 6 · 2022-09-06 07:03:00

147

Views

The equation $x^{4}-3x^{3}-6x^{2}+ax+b=0$ has a triple root. Find $a$ and $b$, and hence all roots of this equation.

Published on 06 Sep 2022 - 7:03

score 91 · Answer 7 · 2022-09-12 22:53:49

91

Views

How to solve square of Quadratic Equation

Published on 12 Sep 2022 - 22:53

score 99 · Answer 8 · 2022-09-20 01:49:44

99

Views

Show that the polynomial $P(x)=x^4-x^2-x+2$ has no real roots

Published on 20 Sep 2022 - 1:49

score 78 · Answer 9 · 2022-09-25 09:50:12

78

Views

How to get roots of this 4th order polynomial given below?

Published on 25 Sep 2022 - 9:50

score 28 · Answer 10 · 2022-09-29 08:07:11

Is there any transformation for the polynomial $x^4+ax^3+bx+1$ to either one of these forms $x^4+cx+d$ or $x^4+cx^3+d$ ? (like brioschi quintic form)

score 767 · Answer 11 · 2022-10-04 23:22:03

767

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Possible "clever" ways to solve $x^4+x^3-2x+1=0$, with methodological justification

Published on 04 Oct 2022 - 23:22

score 223 · Answer 12 · 2022-11-02 04:39:44

223

Views

Olympiad-like way to solve the equation $(x^2-4)(x^2+6x+6)=x^2-1$?

Published on 02 Nov 2022 - 4:39

score 194 · Answer 13 · 2022-11-20 03:34:10

194

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Show that the equation $x^4-8x^3+22x^2-24x+4=0$ has exactly two real roots, both being positive

Published on 20 Nov 2022 - 3:34

score 76 · Answer 14 · 2026-03-26 16:56:44

76

Views

If a hidden quadratic has no real roots, does that mean that the equation it represents also has no real roots?

Published on 26 Mar 2026 - 16:56

score 83 · Answer 15 · 2026-03-19 18:52:11

83

Views

Solvability criteria for a a monic almost palindromic quartic diophantine equation

Published on 19 Mar 2026 - 18:52

List Question

Quartic with only one singular point

Resting a stick in a cup. How far away from the side will it be?

Square roots of root-expressions: distinguishing quartic Galois groups from copies of $C_4$ or of $D_4$ - exercise M.11, Ch.16 Artin's algebra

Prove $f(-\frac12) \le \frac{3}{16}$ if all roots of $f(x) = x^4 - x^3 + a x + b$ are real

is there a cubic or quartic approximation for these data points?

The equation $x^{4}-3x^{3}-6x^{2}+ax+b=0$ has a triple root. Find $a$ and $b$, and hence all roots of this equation.

How to solve square of Quadratic Equation

Show that the polynomial $P(x)=x^4-x^2-x+2$ has no real roots

How to get roots of this 4th order polynomial given below?

Is there any transformation for the polynomial $x^4+ax^3+bx+1$ to either one of these forms $x^4+cx+d$ or $x^4+cx^3+d$ ? (like brioschi quintic form)

Possible "clever" ways to solve $x^4+x^3-2x+1=0$, with methodological justification

Olympiad-like way to solve the equation $(x^2-4)(x^2+6x+6)=x^2-1$?

Show that the equation $x^4-8x^3+22x^2-24x+4=0$ has exactly two real roots, both being positive

If a hidden quadratic has no real roots, does that mean that the equation it represents also has no real roots?

Solvability criteria for a a monic almost palindromic quartic diophantine equation

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