List questions from polynomials

Published on 25 Mar 2026 - 9:50

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Prove: $k^3 - k( b c + c a + a b ) + 2 a b c = 0$ always has a negative root with all positive parameters $a, b, c$

Published on 24 Mar 2026 - 23:46

987

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Roots of polynomials with bounded integer coefficients

Published on 31 Mar 2026 - 5:54

41

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Divisibility conditions

Published on 25 Mar 2026 - 14:39

119

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$\lim_{h\to 0} \frac{ f(a+ h) - 2f(a) + f(a-h) }{h^2}$ and a polynomial function with degree at most 2

Published on 23 Apr 2018 - 19:13

433

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Decomposition of a homogeneous polynomial into a sum of harmonic and $x^2 q$.

Published on 25 Mar 2026 - 1:20

267

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Lower bound on the number of real roots of a polynomial

Published on 30 Mar 2026 - 5:30

83

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Find the remainder when $(x+1)^n$ is divided by $(x-1)^3$.

Published on 26 Mar 2026 - 6:21

72

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solving $ f(x,y,z) = \beta_{111} x y z$

Published on 25 Mar 2026 - 22:10

32

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Finding the number of functions that can be formed.

Published on 24 Apr 2018 - 16:49

32

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To find a relation between $a,b,c$ given a quadratic and a cubic epression

Published on 24 Mar 2026 - 22:09

141

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"Square root" of a decomposition of a homogeneous polynomial to harmonic and $x^2 q$.

Published on 23 Mar 2026 - 8:34

766

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Vandermonde matrix unique solution to polynomial equation

Published on 25 Mar 2026 - 14:19

81

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$r+s√d$ is a root of $x^3-3x-1=0$. Prove that $3r^2s+s^3d-3s = 0$

Published on 25 Apr 2018 - 0:51

80

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Roots of a special polynomial

Published on 30 Mar 2026 - 5:25

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Taylor polynomial and approximation of integral

Prove: $k^3 - k( b c + c a + a b ) + 2 a b c = 0$ always has a negative root with all positive parameters $a, b, c$

Roots of polynomials with bounded integer coefficients

Divisibility conditions

$\lim_{h\to 0} \frac{ f(a+ h) - 2f(a) + f(a-h) }{h^2}$ and a polynomial function with degree at most 2

Decomposition of a homogeneous polynomial into a sum of harmonic and $x^2 q$.

Lower bound on the number of real roots of a polynomial

Find the remainder when $(x+1)^n$ is divided by $(x-1)^3$.

solving $ f(x,y,z) = \beta_{111} x y z$

Finding the number of functions that can be formed.

To find a relation between $a,b,c$ given a quadratic and a cubic epression

"Square root" of a decomposition of a homogeneous polynomial to harmonic and $x^2 q$.

Vandermonde matrix unique solution to polynomial equation

$r+s√d$ is a root of $x^3-3x-1=0$. Prove that $3r^2s+s^3d-3s = 0$

Roots of a special polynomial

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