Question

Find the six complex roots of the equation $f(x)=x^6+8\sqrt{2}x^3+64=0$

score 97 · Answer 1 · 2026-04-16 07:40:01

97

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Find the six complex roots of the equation $f(x)=x^6+8\sqrt{2}x^3+64=0$

Published on 16 Apr 2026 - 7:40

score 82 · Answer 2 · 2026-04-14 23:46:54

82

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Do the roots of these functions have closed-form expressions?

Published on 14 Apr 2026 - 23:46

score 205 · Answer 3 · 2026-03-26 17:53:26

205

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The relation between the number of solution of $f(x)=x$ and $f(f(x))=x$, when f is a quartic polynomial

Published on 26 Mar 2026 - 17:53

score 74 · Answer 4 · 2026-04-09 08:11:48

74

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Understanding a proof of the Open Mapping Theorem

Published on 09 Apr 2026 - 8:11

score 139 · Answer 5 · 2026-04-16 09:15:07

139

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Conjecture: If $f(x)=\prod\limits_{k=1}^n(x-k)$ then $\lim\limits_{n\to\infty}\frac1n [\text{largest root of $f(x)=f'(x)$}]=\frac{e}{e-1}$.

Published on 16 Apr 2026 - 9:15

score 90 · Answer 6 · 2026-03-26 17:53:23

90

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Show that the roots of the equation $b^2(x^4+1)-14b(1+b^2)x(x^2+1)+(1+196b^2+b^4)x^2=0$ are all real and all have the same sign as $b$.

Published on 26 Mar 2026 - 17:53

score 113 · Answer 7 · 2026-03-26 17:53:15

113

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Find $\sin{\frac{\pi}{10}}$ in form of $a+b\sqrt{k}$

Published on 26 Mar 2026 - 17:53

score 23 · Answer 8 · 2026-04-14 11:22:25

23

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Roots of a polynomial over the set of complex numbers

Published on 14 Apr 2026 - 11:22

score 111 · Answer 9 · 2026-04-12 18:14:27

111

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Why does taking the tangent line improve the approximation in Newton's method?

Published on 12 Apr 2026 - 18:14

score 107 · Answer 10 · 2026-04-11 17:48:16

107

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Find the roots of a quadratic equation, with integer coefficients, rounded to nearest integer

Published on 11 Apr 2026 - 17:48

score 75 · Answer 11 · 2026-04-13 23:26:26

75

Views

Is there any real root of the cubic polynomial.

Published on 13 Apr 2026 - 23:26

score 62 · Answer 12 · 2026-04-13 21:05:20

62

Views

Newton's Method convergence for all approximations in $[a,b]$

Published on 13 Apr 2026 - 21:05

score 937 · Answer 13 · 2026-04-14 09:52:40

937

Views

Convex function on the graph but impossible to prove??!

Published on 14 Apr 2026 - 9:52

score 80 · Answer 14 · 2026-04-09 01:30:23

80

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What is $i^{\frac13}$?

Published on 09 Apr 2026 - 1:30

score 89 · Answer 15 · 2026-03-26 16:26:34

89

Views

How many roots in a system of quartic equations

Published on 26 Mar 2026 - 16:26

List Question

Find the six complex roots of the equation $f(x)=x^6+8\sqrt{2}x^3+64=0$

Do the roots of these functions have closed-form expressions?

The relation between the number of solution of $f(x)=x$ and $f(f(x))=x$, when f is a quartic polynomial

Understanding a proof of the Open Mapping Theorem

Conjecture: If $f(x)=\prod\limits_{k=1}^n(x-k)$ then $\lim\limits_{n\to\infty}\frac1n [\text{largest root of $f(x)=f'(x)$}]=\frac{e}{e-1}$.

Show that the roots of the equation $b^2(x^4+1)-14b(1+b^2)x(x^2+1)+(1+196b^2+b^4)x^2=0$ are all real and all have the same sign as $b$.

Find $\sin{\frac{\pi}{10}}$ in form of $a+b\sqrt{k}$

Roots of a polynomial over the set of complex numbers

Why does taking the tangent line improve the approximation in Newton's method?

Find the roots of a quadratic equation, with integer coefficients, rounded to nearest integer

Is there any real root of the cubic polynomial.

Newton's Method convergence for all approximations in $[a,b]$

Convex function on the graph but impossible to prove??!

What is $i^{\frac13}$?

How many roots in a system of quartic equations

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