Question

find $a$ and $b$ where $x^3 - 4x^2 -3x + 18 = (x+a)(x-b)^2$

score 101 · Answer 1 · 2023-10-05 13:28:03

101

Views

find $a$ and $b$ where $x^3 - 4x^2 -3x + 18 = (x+a)(x-b)^2$

Published on 05 Oct 2023 - 13:28

score 42 · Answer 2 · 2023-10-07 13:43:57

42

Views

Prove a relation between the coefficients of a depressed cubic.

Published on 07 Oct 2023 - 13:43

score 72 · Answer 3 · 2023-10-15 21:32:46

72

Views

For translation of axes, is there a definite equation for any of "the 27 lines" on the Clebsch Diagonal Cubic?

Published on 15 Oct 2023 - 21:32

score 570 · Answer 4 · 2026-03-27 23:23:32

Can you tell me about the (probably) well known relationship between the coefficients of a cubic and some features of a rectangular solid?

score 38 · Answer 5 · 2026-02-23 06:40:33

38

Views

Set of coefficients of degree three monic real polynomial with three real roots is connected.

Published on 23 Feb 2026 - 6:40

score 51 · Answer 6 · 2026-03-27 11:38:33

51

Views

Descartes folium

Published on 27 Mar 2026 - 11:38

score 132 · Answer 7 · 2023-11-05 01:26:38

132

Views

Prove $(1+a^3) (1+b^3)(1+c^3) \ge (\frac{ab+bc+ca+1}{2})^3$

Published on 05 Nov 2023 - 1:26

score 37 · Answer 8 · 2023-11-07 01:48:30

37

Views

Disjoint exceptional lines on non-minimal cubic surface

Published on 07 Nov 2023 - 1:48

score 213 · Answer 9 · 2023-11-09 14:24:45

213

Views

More $a^3+b^3+c^3=(c+1)^3,$ and $\sqrt[3]{\cos\tfrac{2\pi}7}+\sqrt[3]{\cos\tfrac{4\pi}7}+\sqrt[3]{\cos\tfrac{8\pi}7}=\sqrt[3]{\tfrac{5-3\sqrt[3]7}2}$

Published on 09 Nov 2023 - 14:24

score 117 · Answer 10 · 2026-03-22 06:06:50

117

Views

Why are all real inflection points on a cubic projective algebraic curve on 1 line?

Published on 22 Mar 2026 - 6:06

score 117 · Answer 11 · 2026-02-23 06:42:30

117

Views

Three real roots of a cubic

Published on 23 Feb 2026 - 6:42

score 160 · Answer 12 · 2026-03-26 08:00:34

160

Views

Prove $2(a+b+c)\left(1+\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\right)\ge 3(a+b)(b+c)(c+a)$ for $abc=1.$

Published on 26 Mar 2026 - 8:00

score 42 · Answer 13 · 2023-12-01 20:20:08

42

Views

Prove this potential cubic theorem/formula

Published on 01 Dec 2023 - 20:20

score 115 · Answer 14 · 2026-03-27 20:31:18

115

Views

There is a compass-like tool that can draw $y=x^2$ on paper. Is there one for $y=x^3$?

Published on 27 Mar 2026 - 20:31

score 100 · Answer 15 · 2026-02-23 06:34:48

100

Views

Prove that $a_3 \lambda^{3} + a_2 \lambda^{2} + a_1 \lambda + a_0 = 0$ has three real roots

Published on 23 Feb 2026 - 6:34

List Question

find $a$ and $b$ where $x^3 - 4x^2 -3x + 18 = (x+a)(x-b)^2$

Prove a relation between the coefficients of a depressed cubic.

For translation of axes, is there a definite equation for any of "the 27 lines" on the Clebsch Diagonal Cubic?

Can you tell me about the (probably) well known relationship between the coefficients of a cubic and some features of a rectangular solid?

Set of coefficients of degree three monic real polynomial with three real roots is connected.

Descartes folium

Prove $(1+a^3) (1+b^3)(1+c^3) \ge (\frac{ab+bc+ca+1}{2})^3$

Disjoint exceptional lines on non-minimal cubic surface

More $a^3+b^3+c^3=(c+1)^3,$ and $\sqrt[3]{\cos\tfrac{2\pi}7}+\sqrt[3]{\cos\tfrac{4\pi}7}+\sqrt[3]{\cos\tfrac{8\pi}7}=\sqrt[3]{\tfrac{5-3\sqrt[3]7}2}$

Why are all real inflection points on a cubic projective algebraic curve on 1 line?

Three real roots of a cubic

Prove $2(a+b+c)\left(1+\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\right)\ge 3(a+b)(b+c)(c+a)$ for $abc=1.$

Prove this potential cubic theorem/formula

There is a compass-like tool that can draw $y=x^2$ on paper. Is there one for $y=x^3$?

Prove that $a_3 \lambda^{3} + a_2 \lambda^{2} + a_1 \lambda + a_0 = 0$ has three real roots

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