Question

Solution to a special type of polynomial equation

score 134 · Answer 1 · 2018-10-14 21:46:54

134

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Solution to a special type of polynomial equation

Published on 14 Oct 2018 - 21:46

score 179 · Answer 2 · 2026-03-31 17:55:34

179

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INMO 1998 question

Published on 31 Mar 2026 - 17:55

score 183 · Answer 3 · 2026-04-01 04:54:59

183

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Prove that if $ab < 0$ then the equation $ax^{3} + bx + c = 0$ has at most three real roots.

Published on 01 Apr 2026 - 4:54

score 170 · Answer 4 · 2026-04-02 11:39:06

170

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A easier way to solve this equation $(z+1)^6+(z-1)^6=0$ in complex field?

Published on 02 Apr 2026 - 11:39

score 58 · Answer 5 · 2026-03-28 20:54:27

58

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Lower bound on the value of a polynomial

Published on 28 Mar 2026 - 20:54

score 1.1k · Answer 6 · 2026-03-29 14:59:13

1.1k

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$\mathbb{Q}(\alpha)=\mathbb{Q}(\beta)$ if $\alpha, \beta$ are algebraic over $\mathbb{Q}$ of degree $2$ and $\alpha +\beta$ is a root of a quadratic.

Published on 29 Mar 2026 - 14:59

score 3.2k · Answer 7 · 2018-10-15 19:00:44

3.2k

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How to find matrix D representing derivative of set of polynomials

Published on 15 Oct 2018 - 19:00

score 45 · Answer 8 · 2018-10-15 19:34:08

45

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Can an algebraic function be written as a composition of polynomials and their inverses?

Published on 15 Oct 2018 - 19:34

score 38 · Answer 9 · 2018-10-16 08:00:30

38

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Need a quadratic function that is larger than zero when variables are unequal

Published on 16 Oct 2018 - 8:00

score 415 · Answer 10 · 2026-03-27 14:03:16

415

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What can be said about the roots of $acx^4 + b(a + c)x^3 + (a^2 + b^2 + c^2 )x^2 + b(a + c)x + ac$?

Published on 27 Mar 2026 - 14:03

score 1.2k · Answer 11 · 2026-03-26 01:23:42

1.2k

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Isomorphism between $K[X]/P(X)$ and $K(A)$ for $A$ a root of the irreducible polynomial $P(X)$ over $K$

Published on 26 Mar 2026 - 1:23

score 422 · Answer 12 · 2026-03-29 18:51:02

422

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Steps towards the Galois group of permutations of the roots of a polynomial

Published on 29 Mar 2026 - 18:51

score 135 · Answer 13 · 2026-03-25 18:51:08

135

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Does $f(x)=x^3+x^2-8x+1$ have rational roots?

Published on 25 Mar 2026 - 18:51

score 541 · Answer 14 · 2018-10-16 18:49:33

541

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Is there a relationship between the eigenvalues of convex combinations of two matrices and roots of convex combination of their polynomials?

Published on 16 Oct 2018 - 18:49

score 122 · Answer 15 · 2026-03-25 11:07:02

122

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Let $F(x)=x^4-bx^3-11x^2+4(b+1)x+a$.Find $a,b$

Published on 25 Mar 2026 - 11:07

List Question

Solution to a special type of polynomial equation

INMO 1998 question

Prove that if $ab < 0$ then the equation $ax^{3} + bx + c = 0$ has at most three real roots.

A easier way to solve this equation $(z+1)^6+(z-1)^6=0$ in complex field?

Lower bound on the value of a polynomial

$\mathbb{Q}(\alpha)=\mathbb{Q}(\beta)$ if $\alpha, \beta$ are algebraic over $\mathbb{Q}$ of degree $2$ and $\alpha +\beta$ is a root of a quadratic.

How to find matrix D representing derivative of set of polynomials

Can an algebraic function be written as a composition of polynomials and their inverses?

Need a quadratic function that is larger than zero when variables are unequal

What can be said about the roots of $acx^4 + b(a + c)x^3 + (a^2 + b^2 + c^2 )x^2 + b(a + c)x + ac$?

Isomorphism between $K[X]/P(X)$ and $K(A)$ for $A$ a root of the irreducible polynomial $P(X)$ over $K$

Steps towards the Galois group of permutations of the roots of a polynomial

Does $f(x)=x^3+x^2-8x+1$ have rational roots?

Is there a relationship between the eigenvalues of convex combinations of two matrices and roots of convex combination of their polynomials?

Let $F(x)=x^4-bx^3-11x^2+4(b+1)x+a$.Find $a,b$

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