Question

Why is it that $x^4+2x^2+1$ is reducible in $\mathbb{Z}[x]$ but has no roots in $\mathbb{Q}$?

score 1.5k · Answer 1 · 2026-04-15 12:08:19

1.5k

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Why is it that $x^4+2x^2+1$ is reducible in $\mathbb{Z}[x]$ but has no roots in $\mathbb{Q}$?

Published on 15 Apr 2026 - 12:08

score 6.9k · Answer 2 · 2026-04-15 14:45:19

6.9k

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If coefficients of the Quadratic Equation are in AP find $\alpha+\beta +\alpha\beta$.

Published on 15 Apr 2026 - 14:45

score 112 · Answer 3 · 2026-04-17 07:55:17

112

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Find that solution satisfying $ϕ$ satisfying $ϕ(0) = 0$, $ϕ'(0) = 1$, $ϕ''(0)=0$ for $y'''-4y'=0$.

Published on 17 Apr 2026 - 7:55

score 239 · Answer 4 · 2026-04-13 22:48:48

239

Views

Methods of approximating polynomial roots

Published on 13 Apr 2026 - 22:48

score 937 · Answer 5 · 2026-04-14 00:35:29

937

Views

Is there a list of common identities for principal branches of complex logarithms and roots?

Published on 14 Apr 2026 - 0:35

score 103 · Answer 6 · 2026-04-16 23:21:44

103

Views

Prove that the roots of a given polynomial don't have the same absolute value

Published on 16 Apr 2026 - 23:21

score 6.5k · Answer 7 · 2026-04-16 14:53:06

6.5k

Views

Counting the Number of Real Roots of $y^{3}-3y+1$

Published on 16 Apr 2026 - 14:53

score 165 · Answer 8 · 2026-04-12 05:04:55

165

Views

Looping through zeroes in polynomials

Published on 12 Apr 2026 - 5:04

score 290 · Answer 9 · 2026-04-11 11:40:41

290

Views

How to find the root of a differential equation when it is exponential?

Published on 11 Apr 2026 - 11:40

score 121 · Answer 10 · 2026-04-15 10:19:13

121

Views

Is the following number not a Pisot-Vijayaraghavan number?

Published on 15 Apr 2026 - 10:19

score 117 · Answer 11 · 2026-04-13 07:37:54

117

Views

Cubic Root verification

Published on 13 Apr 2026 - 7:37

score 61 · Answer 12 · 2026-04-15 11:22:12

61

Views

Find root of equation $\frac{2bnx}{a\sqrt{x^2-b^2}}+\frac{2bx}{a}+\frac{2ax}{b}-2m=0$

Published on 15 Apr 2026 - 11:22

score 66 · Answer 13 · 2026-04-12 07:58:51

66

Views

Quadratic Equations and their Roots

Published on 12 Apr 2026 - 7:58

score 113 · Answer 14 · 2026-04-14 07:59:46

113

Views

Proving relation with zeros of holomorphic functions

Published on 14 Apr 2026 - 7:59

score 57 · Answer 15 · 2026-04-17 15:15:48

57

Views

Find value or $W=\sqrt[4x+4]{3^{x}\left ( \sqrt{5}-1 \right )}$ according to condition $9^{x}=6^x +4^x$

Published on 17 Apr 2026 - 15:15

List Question

Why is it that $x^4+2x^2+1$ is reducible in $\mathbb{Z}[x]$ but has no roots in $\mathbb{Q}$?

If coefficients of the Quadratic Equation are in AP find $\alpha+\beta +\alpha\beta$.

Find that solution satisfying $ϕ$ satisfying $ϕ(0) = 0$, $ϕ'(0) = 1$, $ϕ''(0)=0$ for $y'''-4y'=0$.

Methods of approximating polynomial roots

Is there a list of common identities for principal branches of complex logarithms and roots?

Prove that the roots of a given polynomial don't have the same absolute value

Counting the Number of Real Roots of $y^{3}-3y+1$

Looping through zeroes in polynomials

How to find the root of a differential equation when it is exponential?

Is the following number not a Pisot-Vijayaraghavan number?

Cubic Root verification

Find root of equation $\frac{2bnx}{a\sqrt{x^2-b^2}}+\frac{2bx}{a}+\frac{2ax}{b}-2m=0$

Quadratic Equations and their Roots

Proving relation with zeros of holomorphic functions

Find value or $W=\sqrt[4x+4]{3^{x}\left ( \sqrt{5}-1 \right )}$ according to condition $9^{x}=6^x +4^x$

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