Question

The minimum number of non real roots of the equation $x^4-2x^3+2x^2-x=k$ is?

score 805 · Answer 1 · 2026-04-17 13:05:18

805

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The minimum number of non real roots of the equation $x^4-2x^3+2x^2-x=k$ is?

Published on 17 Apr 2026 - 13:05

score 355 · Answer 2 · 2026-04-23 07:17:12

355

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How can one find the zeroes of $f(x)=ae^{bx}+cx+d$?

Published on 23 Apr 2026 - 7:17

score 310 · Answer 3 · 2026-04-16 01:46:46

310

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$x^n+a_{n-1}x^{n-1}+\cdots +a_1x+a_0=0$ has real coefficients which satisfy $0<a_0 \le a_1 \le \cdots \le a_{n-1} \le 1$ prove that $z$ is a root

Published on 16 Apr 2026 - 1:46

score 54 · Answer 4 · 2026-04-11 17:54:29

54

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Zeros of a sum of real powers

Published on 11 Apr 2026 - 17:54

score 406 · Answer 5 · 2026-04-15 21:31:24

406

Views

Why is $x=2 \implies (x-2)(x-3)=0$ false?

Published on 15 Apr 2026 - 21:31

score 30 · Answer 6 · 2026-04-14 12:24:21

30

Views

Combining the rule of signs and index shifting.

Published on 14 Apr 2026 - 12:24

score 74 · Answer 7 · 2026-04-25 08:55:40

74

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Why are the factors of some solutions to a Pell equation also a solution?

Published on 25 Apr 2026 - 8:55

score 450 · Answer 8 · 2026-04-14 13:36:39

450

Views

Factorize polynomial in Matlab

Published on 14 Apr 2026 - 13:36

score 802 · Answer 9 · 2026-04-17 13:05:55

802

Views

Theorem 1.21 in Baby Rudin: How do we obtain $\sqrt[m]{\sqrt[n]{a}}=\sqrt[mn]{a}$ for any $a>0$ and $m, n \in \mathbb{N}$?

Published on 17 Apr 2026 - 13:05

score 1.6k · Answer 10 · 2026-04-07 12:04:24

1.6k

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Applying trigonometry in solving quintic polynomials?

Published on 07 Apr 2026 - 12:04

score 1.9k · Answer 11 · 2026-03-30 02:07:05

1.9k

Views

Show that the roots of P' lie in the same half plane as the roots of P

Published on 30 Mar 2026 - 2:07

score 213 · Answer 12 · 2026-03-27 08:56:01

213

Views

The general solution of $x^a = a^x$ for real $a >0$

Published on 27 Mar 2026 - 8:56

score 172 · Answer 13 · 2026-04-13 23:06:13

172

Views

Algebra: Rational roots of a polynomial of degree $4$

Published on 13 Apr 2026 - 23:06

score 11.3k · Answer 14 · 2026-04-10 00:17:02

11.3k

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How to find no. of complex root of any polynomial?

Published on 10 Apr 2026 - 0:17

score 383 · Answer 15 · 2026-04-17 00:47:25

383

Views

Geometric solution of quintic equations

Published on 17 Apr 2026 - 0:47

List Question

The minimum number of non real roots of the equation $x^4-2x^3+2x^2-x=k$ is?

How can one find the zeroes of $f(x)=ae^{bx}+cx+d$?

$x^n+a_{n-1}x^{n-1}+\cdots +a_1x+a_0=0$ has real coefficients which satisfy $0<a_0 \le a_1 \le \cdots \le a_{n-1} \le 1$ prove that $z$ is a root

Zeros of a sum of real powers

Why is $x=2 \implies (x-2)(x-3)=0$ false?

Combining the rule of signs and index shifting.

Why are the factors of some solutions to a Pell equation also a solution?

Factorize polynomial in Matlab

Theorem 1.21 in Baby Rudin: How do we obtain $\sqrt[m]{\sqrt[n]{a}}=\sqrt[mn]{a}$ for any $a>0$ and $m, n \in \mathbb{N}$?

Applying trigonometry in solving quintic polynomials?

Show that the roots of P' lie in the same half plane as the roots of P

The general solution of $x^a = a^x$ for real $a >0$

Algebra: Rational roots of a polynomial of degree $4$

How to find no. of complex root of any polynomial?

Geometric solution of quintic equations

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