Question

If $\alpha,\beta,\gamma$ are the roots of $x^3+x^2-x+1=0$, find the value of $\prod\left(\frac1{\alpha^3}+\frac1{\beta^3}-\frac1{\gamma^3}\right)$

score 283 · Answer 1 · 2022-01-24 19:32:23

283

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If $\alpha,\beta,\gamma$ are the roots of $x^3+x^2-x+1=0$, find the value of $\prod\left(\frac1{\alpha^3}+\frac1{\beta^3}-\frac1{\gamma^3}\right)$

Published on 24 Jan 2022 - 19:32

score 403 · Answer 2 · 2026-03-25 07:30:10

403

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Understanding Cardano's Formula

Published on 25 Mar 2026 - 7:30

score 69 · Answer 3 · 2022-01-26 14:29:30

69

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A perplexity over the cubic root.

Published on 26 Jan 2022 - 14:29

score 194 · Answer 4 · 2022-02-03 23:02:52

194

Views

Clarification about solving cubic equations

Published on 03 Feb 2022 - 23:02

score 147 · Answer 5 · 2022-02-05 12:14:59

147

Views

Alternative Solution for Cubic Equation

Published on 05 Feb 2022 - 12:14

score 323 · Answer 6 · 2022-02-09 10:23:13

323

Views

Find $a, b, c$ such that $a^3+b^3+c^3-3abc=2017$.

Published on 09 Feb 2022 - 10:23

score 240 · Answer 7 · 2022-02-13 05:59:33

240

Views

Condition for real roots of depressed cubic equation

Published on 13 Feb 2022 - 5:59

score 137 · Answer 8 · 2026-03-26 15:16:55

137

Views

What are the necessary and sufficient conditions for the cubic equation to have at least 1 positive real root?

Published on 26 Mar 2026 - 15:16

score 90 · Answer 9 · 2022-02-20 21:56:49

90

Views

Stuck on simplifying expressions involving trig and inverse trig functions

Published on 20 Feb 2022 - 21:56

score 94 · Answer 10 · 2022-03-01 12:06:08

94

Views

solve this formula for $x$: $y = \frac{5x(2x^2 + 27x + 89)}{6}$

Published on 01 Mar 2022 - 12:06

score 202 · Answer 11 · 2022-03-02 17:53:13

202

Views

Cubic polynomial without $x^1$

Published on 02 Mar 2022 - 17:53

score 158 · Answer 12 · 2022-03-04 16:11:19

158

Views

$f(x)$ and $g(x)$ are monic cubic polynomials, with $f(x)-g(x)=r$. If $f$ has roots $r+1$ and $r+7$, and $g$ has roots $r+3$ and $r+9$, then find $r$.

Published on 04 Mar 2022 - 16:11

score 47 · Answer 13 · 2022-03-14 10:31:36

47

Views

How to factor $z^3-3\sqrt{3}iz^2-9z+3\sqrt{3}i$ strictly via the method of grouping

Published on 14 Mar 2022 - 10:31

score 46 · Answer 14 · 2026-03-28 22:25:25

46

Views

Find a cubic function given the inflection point and minimal point

Published on 28 Mar 2026 - 22:25

score 605 · Answer 15 · 2022-03-25 10:42:28

605

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Inverse a cubic function

Published on 25 Mar 2022 - 10:42

List Question

If $\alpha,\beta,\gamma$ are the roots of $x^3+x^2-x+1=0$, find the value of $\prod\left(\frac1{\alpha^3}+\frac1{\beta^3}-\frac1{\gamma^3}\right)$

Understanding Cardano's Formula

A perplexity over the cubic root.

Clarification about solving cubic equations

Alternative Solution for Cubic Equation

Find $a, b, c$ such that $a^3+b^3+c^3-3abc=2017$.

Condition for real roots of depressed cubic equation

What are the necessary and sufficient conditions for the cubic equation to have at least 1 positive real root?

Stuck on simplifying expressions involving trig and inverse trig functions

solve this formula for $x$: $y = \frac{5x(2x^2 + 27x + 89)}{6}$

Cubic polynomial without $x^1$

$f(x)$ and $g(x)$ are monic cubic polynomials, with $f(x)-g(x)=r$. If $f$ has roots $r+1$ and $r+7$, and $g$ has roots $r+3$ and $r+9$, then find $r$.

How to factor $z^3-3\sqrt{3}iz^2-9z+3\sqrt{3}i$ strictly via the method of grouping

Find a cubic function given the inflection point and minimal point

Inverse a cubic function

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