Question

If $x^4+12x-5$ has roots $x_1,x_2,x_3,x_4$ find polynomial with roots $x_1+x_2,x_1+x_3,x_1+x_4,x_2+x_3,x_2+x_4,x_3+x_4$

score 232 · Answer 1 · 2020-03-09 06:04:53

232

Views

If $x^4+12x-5$ has roots $x_1,x_2,x_3,x_4$ find polynomial with roots $x_1+x_2,x_1+x_3,x_1+x_4,x_2+x_3,x_2+x_4,x_3+x_4$

Published on 09 Mar 2020 - 6:04

score 33 · Answer 2 · 2026-04-02 13:01:54

33

Views

Knowing one $0$ of a quadratic trin., can I determine some necessary ( or sufficient) condition regarding the second root, in terms of the first one?

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score 68 · Answer 3 · 2026-03-31 03:29:03

68

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48

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score 69 · Answer 5 · 2020-03-10 14:12:05

69

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Why does this pattern occur on this plot?

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score 37 · Answer 6 · 2026-04-02 14:49:35

37

Views

How to do a quick estimation if $x_2 \ll x_1$ holds for the roots of a quadratic equation - to apply quick and easy root-finding formula?

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score 612 · Answer 7 · 2026-03-26 01:07:48

612

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score 82 · Answer 8 · 2026-03-26 18:58:53

82

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96

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score 86 · Answer 10 · 2026-03-27 11:24:42

86

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score 61 · Answer 11 · 2026-04-02 14:49:35

61

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score 71 · Answer 12 · 2020-03-15 15:54:58

71

Views

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score 587 · Answer 13 · 2026-03-26 19:02:09

587

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score 73 · Answer 14 · 2020-03-16 00:28:46

Given the polynomial $x^5 + a^2 x^4 + 1 = 0$, find the set of values of $a$ such that $2$ of the roots have negative imaginary part.

score 59 · Answer 15 · 2026-02-23 10:47:21

59

Views

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Published on 23 Feb 2026 - 10:47

List Question

If $x^4+12x-5$ has roots $x_1,x_2,x_3,x_4$ find polynomial with roots $x_1+x_2,x_1+x_3,x_1+x_4,x_2+x_3,x_2+x_4,x_3+x_4$

Knowing one $0$ of a quadratic trin., can I determine some necessary ( or sufficient) condition regarding the second root, in terms of the first one?

Is ${(-1)}^{\frac{1}{6}}=i$?

About rational root theorem in factoring

Why does this pattern occur on this plot?

How to do a quick estimation if $x_2 \ll x_1$ holds for the roots of a quadratic equation - to apply quick and easy root-finding formula?

Possible formula for $\sum_{} (\alpha\beta)^2$ and $\sum_{} \alpha\beta(\alpha+\beta)$

Using vieta’s formula to make a cubic using roots

Polynomial problem TUGMOs Grade9

TUGMOs2012 grade9 equation

Roots of quadratic with $a$ and $8a+3b+c$ of the same sign cannot lie in (2,4)

Estimate for the root of a polynomial-like expression

Can I solve this other than using Newton's sums or Newton's identities?

Given the polynomial $x^5 + a^2 x^4 + 1 = 0$, find the set of values of $a$ such that $2$ of the roots have negative imaginary part.

Help to find the roots of an inverse trigonometric function

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