Question

Conditioning of the calculation of roots for cubic polynomial

score 405 · Answer 1 · 2014-12-06 15:50:29

405

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Conditioning of the calculation of roots for cubic polynomial

Published on 06 Dec 2014 - 15:50

score 594 · Answer 2 · 2014-12-06 21:43:39

594

Views

Show all roots of $\sum_{k=0}^n 2^{k(n-k)} x^k$ are real (December 6, 2014 Putnam problem)

Published on 06 Dec 2014 - 21:43

score 46 · Answer 3 · 2014-12-06 22:46:52

46

Views

Solving for $x$ using $\ln$ or any possible way.

Published on 06 Dec 2014 - 22:46

score 120 · Answer 4 · 2026-03-30 07:20:43

120

Views

Applying Newton-Raphson method to $a\cdot b^{-2}=c\cdot d^4+e\cdot f(d)$

Published on 30 Mar 2026 - 7:20

score 464 · Answer 5 · 2014-12-08 02:00:17

464

Views

Sum of square of absolute values of roots of a polynomial

Published on 08 Dec 2014 - 2:00

score 78 · Answer 6 · 2026-04-01 21:08:52

78

Views

Solving $3t^2-\frac{12}{3}t+\frac{4}{3}=0$

Published on 01 Apr 2026 - 21:08

score 220 · Answer 7 · 2014-12-08 18:00:06

220

Views

$f'(a)=0$ implies $x=a$ is not a simple zero of $f$

Published on 08 Dec 2014 - 18:00

score 51 · Answer 8 · 2014-12-08 18:18:28

51

Views

Find a solution for an equation

Published on 08 Dec 2014 - 18:18

score 139 · Answer 9 · 2014-12-09 01:56:40

139

Views

Roots of a polynomial equation where coefficients follow a geometric progression

Published on 09 Dec 2014 - 1:56

score 90 · Answer 10 · 2014-12-09 12:14:03

90

Views

Proving $x=\sqrt{a}+\sqrt{b}$ is the key root to solve $x^4-2(a+b)x^2+(a-b)^2=0$

Published on 09 Dec 2014 - 12:14

score 10.8k · Answer 11 · 2014-12-09 18:45:28

10.8k

Views

how many distinct real zeros a function has

Published on 09 Dec 2014 - 18:45

score 71 · Answer 12 · 2026-03-26 19:17:09

71

Views

Find the equation which has key root $x=\sqrt{a}+\sqrt{b}+\sqrt{c}$

Published on 26 Mar 2026 - 19:17

score 2.6k · Answer 13 · 2014-12-11 21:00:31

2.6k

Views

$x^4 + x^2 + 1 = 0$ has no solution in $\mathbb{R}$.

Published on 11 Dec 2014 - 21:00

score 61 · Answer 14 · 2014-12-12 05:12:16

61

Views

A problem related to complex polynomial

Published on 12 Dec 2014 - 5:12

score 1.2k · Answer 15 · 2026-03-30 08:00:12

1.2k

Views

Evaluate this Trigonometric Expression: $\sqrt[3]{\cos \frac{2\pi}{7}} + \sqrt[3]{\cos \frac{4\pi}{7}} + \sqrt[3]{\cos \frac{6\pi}{7}}$

Published on 30 Mar 2026 - 8:00

List Question

Conditioning of the calculation of roots for cubic polynomial

Show all roots of $\sum_{k=0}^n 2^{k(n-k)} x^k$ are real (December 6, 2014 Putnam problem)

Solving for $x$ using $\ln$ or any possible way.

Applying Newton-Raphson method to $a\cdot b^{-2}=c\cdot d^4+e\cdot f(d)$

Sum of square of absolute values of roots of a polynomial

Solving $3t^2-\frac{12}{3}t+\frac{4}{3}=0$

$f'(a)=0$ implies $x=a$ is not a simple zero of $f$

Find a solution for an equation

Roots of a polynomial equation where coefficients follow a geometric progression

Proving $x=\sqrt{a}+\sqrt{b}$ is the key root to solve $x^4-2(a+b)x^2+(a-b)^2=0$

how many distinct real zeros a function has

Find the equation which has key root $x=\sqrt{a}+\sqrt{b}+\sqrt{c}$

$x^4 + x^2 + 1 = 0$ has no solution in $\mathbb{R}$.

A problem related to complex polynomial

Evaluate this Trigonometric Expression: $\sqrt[3]{\cos \frac{2\pi}{7}} + \sqrt[3]{\cos \frac{4\pi}{7}} + \sqrt[3]{\cos \frac{6\pi}{7}}$

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