Question

How can I find the real roots of $x^4-x^2+1$?

score 514 · Answer 1 · 2026-03-25 07:52:27

514

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How can I find the real roots of $x^4-x^2+1$?

Published on 25 Mar 2026 - 7:52

score 177 · Answer 2 · 2018-10-13 11:25:23

177

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If natural number $n$ doesn't has the form of $k^{m}$, for natural $k$ and $m$, then $x^{m}=n$ has no rational root.

Published on 13 Oct 2018 - 11:25

score 54 · Answer 3 · 2026-03-25 14:06:04

54

Views

Rational $F_n$ Limit $\to$ Find Denominator Polynomial

Published on 25 Mar 2026 - 14:06

score 34 · Answer 4 · 2026-03-25 14:02:00

34

Views

Limits Rational Fn missing p and q

Published on 25 Mar 2026 - 14:02

score 85 · Answer 5 · 2026-03-26 19:11:53

85

Views

Show that $ Ax^2 + x + 1 = 0 $ has roots greater than $1$ given $-1<A<0$

Published on 26 Mar 2026 - 19:11

score 91 · Answer 6 · 2018-10-14 08:48:38

91

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Is $i$ a 3rd root of $-i$

Published on 14 Oct 2018 - 8:48

score 1.3k · Answer 7 · 2018-10-14 12:23:55

1.3k

Views

How many possible rational roots are there for $2x^4 + 4x^3 - 6x^2 + 15x - 12 = 0$?

Published on 14 Oct 2018 - 12:23

score 1.3k · Answer 8 · 2026-03-24 22:07:44

1.3k

Views

Show that $f_a(z)=z+a-e^z$ has only 1 zero in $Re(z)<0$ and this zero is $<0$. $(a>1)$

Published on 24 Mar 2026 - 22:07

score 182 · Answer 9 · 2018-10-15 07:43:28

182

Views

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

Published on 15 Oct 2018 - 7:43

score 251 · Answer 10 · 2026-03-29 18:51:02

If $\alpha,\beta\in C$ are algebraic over $Q$, show that $\alpha+\beta$ is a root of a quadratic polynomial in $Q[x]$ (with conditions).

score 1.1k · Answer 11 · 2026-03-29 14:59:13

1.1k

Views

$\mathbb{Q}(\alpha)=\mathbb{Q}(\beta)$ 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 78 · Answer 12 · 2026-03-26 16:05:58

78

Views

Find count of this functions roots:$\sqrt{x+1}-x^2+1=0$

Published on 26 Mar 2026 - 16:05

score 493 · Answer 13 · 2026-03-27 00:02:15

493

Views

Calculation cube root by hand using division method, not working for $\sqrt[3]{4} $

Published on 27 Mar 2026 - 0:02

score 96 · Answer 14 · 2018-10-15 18:34:29

96

Views

Just find number of its roots: $\sin{x}-x\cos{x}=0$

Published on 15 Oct 2018 - 18:34

score 444 · Answer 15 · 2026-03-25 21:01:32

444

Views

Is there a closed form expression for the first zero of the first Bessel function?

Published on 25 Mar 2026 - 21:01

List Question

How can I find the real roots of $x^4-x^2+1$?

If natural number $n$ doesn't has the form of $k^{m}$, for natural $k$ and $m$, then $x^{m}=n$ has no rational root.

Rational $F_n$ Limit $\to$ Find Denominator Polynomial

Limits Rational Fn missing p and q

Show that $ Ax^2 + x + 1 = 0 $ has roots greater than $1$ given $-1<A<0$

Is $i$ a 3rd root of $-i$

How many possible rational roots are there for $2x^4 + 4x^3 - 6x^2 + 15x - 12 = 0$?

Show that $f_a(z)=z+a-e^z$ has only 1 zero in $Re(z)<0$ and this zero is $<0$. $(a>1)$

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

If $\alpha,\beta\in C$ are algebraic over $Q$, show that $\alpha+\beta$ is a root of a quadratic polynomial in $Q[x]$ (with conditions).

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

Find count of this functions roots:$\sqrt{x+1}-x^2+1=0$

Calculation cube root by hand using division method, not working for $\sqrt[3]{4} $

Just find number of its roots: $\sin{x}-x\cos{x}=0$

Is there a closed form expression for the first zero of the first Bessel function?

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