Question

I need some help with this question: let $p,q,r,s$ be the roots of $3x^4 - x + 12 = 0$, find $pqr + pqs + prs + qrs$

score 71 · Answer 1 · 2026-04-15 22:17:52

71

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I need some help with this question: let $p,q,r,s$ be the roots of $3x^4 - x + 12 = 0$, find $pqr + pqs + prs + qrs$

Published on 15 Apr 2026 - 22:17

score 150 · Answer 2 · 2026-04-16 14:34:37

150

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Find the number of real roots of the polynomial: $f(x)=x^{11}-14x+19$?

Published on 16 Apr 2026 - 14:34

score 76 · Answer 3 · 2026-04-11 02:28:58

76

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How to reliably find the global minimum of a rational function?

Published on 11 Apr 2026 - 2:28

score 77 · Answer 4 · 2026-04-12 04:37:44

77

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Infinite series expansion for roots

Published on 12 Apr 2026 - 4:37

score 93 · Answer 5 · 2026-04-12 06:53:58

93

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Proving the existence of a root, with an unidentified f(x)

Published on 12 Apr 2026 - 6:53

score 57 · Answer 6 · 2026-04-17 12:05:07

57

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Can I approximate $\rho_n$ somehow so it satisfies this Bessel function conidition?

Published on 17 Apr 2026 - 12:05

score 109 · Answer 7 · 2026-04-14 15:02:03

Why do the zeros of $\frac{(\phi^z)-(-1/\phi)^z}{\sqrt{5}}$, where $z$ is complex and $\phi$ is the Golden Ratio, appear on a line?

score 57 · Answer 8 · 2026-04-16 02:36:42

57

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Find sum of roots of following equation

Published on 16 Apr 2026 - 2:36

score 72 · Answer 9 · 2026-04-16 15:18:32

72

Views

Proving $x^{1/1} = x$

Published on 16 Apr 2026 - 15:18

score 75 · Answer 10 · 2026-04-16 12:13:38

75

Views

Trick to solve quadratic mixed with surds

Published on 16 Apr 2026 - 12:13

score 60 · Answer 11 · 2026-04-09 09:35:19

60

Views

A lower bound of the distance between 2 distinct roots of 2 distinct polynomials

Published on 09 Apr 2026 - 9:35

score 59 · Answer 12 · 2026-04-08 14:00:29

59

Views

Can we determine the divisibility of a polynomial by another polynomial from their roots?

Published on 08 Apr 2026 - 14:00

score 65 · Answer 13 · 2026-04-13 03:09:01

65

Views

Theorem 6, Section 3.6 of Hungerford’s Abstract Algebra

Published on 13 Apr 2026 - 3:09

score 3.6k · Answer 14 · 2026-04-12 14:07:59

3.6k

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Does Newton's method converge for all polynomials?

Published on 12 Apr 2026 - 14:07

score 102 · Answer 15 · 2026-04-17 05:11:12

102

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Let $P(x)$ be a polynomial of degree $m>0$ with nonzero coefficients. Prove that $P(x)=\cos(x)$ can have exactly $n$ roots.

Published on 17 Apr 2026 - 5:11

List Question

I need some help with this question: let $p,q,r,s$ be the roots of $3x^4 - x + 12 = 0$, find $pqr + pqs + prs + qrs$

Find the number of real roots of the polynomial: $f(x)=x^{11}-14x+19$?

How to reliably find the global minimum of a rational function?

Infinite series expansion for roots

Proving the existence of a root, with an unidentified f(x)

Can I approximate $\rho_n$ somehow so it satisfies this Bessel function conidition?

Why do the zeros of $\frac{(\phi^z)-(-1/\phi)^z}{\sqrt{5}}$, where $z$ is complex and $\phi$ is the Golden Ratio, appear on a line?

Find sum of roots of following equation

Proving $x^{1/1} = x$

Trick to solve quadratic mixed with surds

A lower bound of the distance between 2 distinct roots of 2 distinct polynomials

Can we determine the divisibility of a polynomial by another polynomial from their roots?

Theorem 6, Section 3.6 of Hungerford’s Abstract Algebra

Does Newton's method converge for all polynomials?

Let $P(x)$ be a polynomial of degree $m>0$ with nonzero coefficients. Prove that $P(x)=\cos(x)$ can have exactly $n$ roots.

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