Question

Prove atleast one of the equations $x^2+b_1x+c_1=0$ and $x^2+b_2x+c_2=0$ has real roots if $b_1b_2=2(c_1+c_2)$

score 48 · Answer 1 · 2026-04-17 05:22:18

48

Views

Prove atleast one of the equations $x^2+b_1x+c_1=0$ and $x^2+b_2x+c_2=0$ has real roots if $b_1b_2=2(c_1+c_2)$

Published on 17 Apr 2026 - 5:22

score 171 · Answer 2 · 2026-04-16 05:11:45

171

Views

Show that $x^p - m$ is irreducible for prime $p$ and $m \in \mathbb{Q^{\times}}\setminus \left(\mathbb{Q^{\times}}\right)^p$

Published on 16 Apr 2026 - 5:11

score 151 · Answer 3 · 2026-04-14 18:31:48

151

Views

does the equation $f_1^3 + f_2^2 = f_3^4$ have a solution in homogeneous polynomials?

Published on 14 Apr 2026 - 18:31

score 631 · Answer 4 · 2026-04-10 11:04:04

631

Views

How do I solve this polynomial equation in $x$ and $y$?

Published on 10 Apr 2026 - 11:04

score 391 · Answer 5 · 2026-04-13 22:35:49

391

Views

Galois group over the field $\mathbb{C}(t)$

Published on 13 Apr 2026 - 22:35

score 889 · Answer 6 · 2026-04-13 19:31:04

889

Views

Rewriting $f(x) = 2x^3+7x^2-14x-40$ as the product of three linear factors

Published on 13 Apr 2026 - 19:31

score 77 · Answer 7 · 2026-04-12 05:08:13

77

Views

How to find the real positive root of $x^{k/2} - x - 1$.

Published on 12 Apr 2026 - 5:08

score 22 · Answer 8 · 2026-04-13 08:03:55

22

Views

Arguing when a system of differential equations can have $n$ critical points.

Published on 13 Apr 2026 - 8:03

score 73 · Answer 9 · 2026-04-09 11:27:27

73

Views

Finding value of constants given an equation and the equation rewritten with constants

Published on 09 Apr 2026 - 11:27

score 165 · Answer 10 · 2026-04-17 00:47:49

165

Views

Given $\cos 3\theta = 4(\cos\theta)^3 - 3\cos\theta$, solve $4x^3 - 9x - 1 = 0$, correct to 3 decimal places.

Published on 17 Apr 2026 - 0:47

score 422 · Answer 11 · 2026-04-16 12:11:49

422

Views

Find the first $3$ orthogonal polynomials of Laguerre (in relation to $\langle f,g\rangle = \int_0^{\infty} f(x)g(x)e^{-x}\ dx$)

Published on 16 Apr 2026 - 12:11

score 40 · Answer 12 · 2026-04-14 07:42:14

40

Views

The extension $k(x)$ over $k(x^p)$ has degree $p$

Published on 14 Apr 2026 - 7:42

score 1.1k · Answer 13 · 2026-04-14 13:21:06

1.1k

Views

Does the degree of a polynomial give the number of roots?

Published on 14 Apr 2026 - 13:21

score 90 · Answer 14 · 2026-04-15 20:04:13

90

Views

Check the properties of given polynomial of order $7$

Published on 15 Apr 2026 - 20:04

score 39 · Answer 15 · 2026-04-17 02:14:02

39

Views

How to compute the maximum of $f(x)=\prod_{i=0}^3(x-x_i)$ $x_i = x_0 + ih$, for $i = 1, 2, 3$, and $h>0$

Published on 17 Apr 2026 - 2:14

List Question

Prove atleast one of the equations $x^2+b_1x+c_1=0$ and $x^2+b_2x+c_2=0$ has real roots if $b_1b_2=2(c_1+c_2)$

Show that $x^p - m$ is irreducible for prime $p$ and $m \in \mathbb{Q^{\times}}\setminus \left(\mathbb{Q^{\times}}\right)^p$

does the equation $f_1^3 + f_2^2 = f_3^4$ have a solution in homogeneous polynomials?

How do I solve this polynomial equation in $x$ and $y$?

Galois group over the field $\mathbb{C}(t)$

Rewriting $f(x) = 2x^3+7x^2-14x-40$ as the product of three linear factors

How to find the real positive root of $x^{k/2} - x - 1$.

Arguing when a system of differential equations can have $n$ critical points.

Finding value of constants given an equation and the equation rewritten with constants

Given $\cos 3\theta = 4(\cos\theta)^3 - 3\cos\theta$, solve $4x^3 - 9x - 1 = 0$, correct to 3 decimal places.

Find the first $3$ orthogonal polynomials of Laguerre (in relation to $\langle f,g\rangle = \int_0^{\infty} f(x)g(x)e^{-x}\ dx$)

The extension $k(x)$ over $k(x^p)$ has degree $p$

Does the degree of a polynomial give the number of roots?

Check the properties of given polynomial of order $7$

How to compute the maximum of $f(x)=\prod_{i=0}^3(x-x_i)$ $x_i = x_0 + ih$, for $i = 1, 2, 3$, and $h>0$

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