Question

Using sum-to-product formula to solve $\sin(2\theta)+\sin(4\theta)=0$

score 415 · Answer 1 · 2020-07-02 22:57:34

415

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Using sum-to-product formula to solve $\sin(2\theta)+\sin(4\theta)=0$

Published on 02 Jul 2020 - 22:57

score 127 · Answer 2 · 2020-07-02 23:08:52

127

Views

Sturm's theorem giving wrong answer for a particular exponential polynomial?

Published on 02 Jul 2020 - 23:08

score 137 · Answer 3 · 2026-03-30 10:54:36

137

Views

Is there such polynomials that exist?

Published on 30 Mar 2026 - 10:54

score 186 · Answer 4 · 2026-04-11 05:24:52

186

Views

Is the set of all monic polynomials in $\mathbb{C}[X]$ with roots in a compact set $K$ compact?

Published on 11 Apr 2026 - 5:24

score 336 · Answer 5 · 2026-04-08 06:25:41

336

Views

Is Po-Shen Loh's trick for roots efficient?

Published on 08 Apr 2026 - 6:25

score 67 · Answer 6 · 2026-04-11 02:14:05

67

Views

Unable to finish a proof for existence of $n$-th roots

Published on 11 Apr 2026 - 2:14

score 1.4k · Answer 7 · 2020-07-06 19:46:22

1.4k

Views

Find all $z$ such that $(z+1)^7 = z^7$. You do not have to put your answer in the simplest rectangular or exponential form.

Published on 06 Jul 2020 - 19:46

score 147 · Answer 8 · 2020-07-06 21:31:25

147

Views

Is $f(x) = 0 \implies f'(x) > 0$ a sufficient condition for uniqueness of roots for a smooth (non constant) function $f$?

Published on 06 Jul 2020 - 21:31

score 277 · Answer 9 · 2020-07-07 08:39:32

277

Views

Let $f$ be continuous. If $f(x) = 0 \implies f$ is strictly increasing at $x$, then $f$ has at most one root.

Published on 07 Jul 2020 - 8:39

score 37 · Answer 10 · 2026-04-08 20:07:58

37

Views

Solution of quadratic equation in matrix notation

Published on 08 Apr 2026 - 20:07

score 290 · Answer 11 · 2020-07-07 18:39:01

290

Views

Consider the sum $S=\sum\frac{1}{x^2}$ which is over all the positive real solutions of the equation $\frac{\tan{x}}{x}=n$

Published on 07 Jul 2020 - 18:39

score 813 · Answer 12 · 2020-07-08 04:39:51

813

Views

If $f(x)= (x-a)(x-b)$ for then the minimum number of roots of equation $\pi(f'(x))^2 \cos(\pi(f(x))) + \sin(\pi(f(x)))f''(x) =0$

Published on 08 Jul 2020 - 4:39

score 56 · Answer 13 · 2026-04-10 08:30:24

56

Views

Finding roots for algebraic equation

Published on 10 Apr 2026 - 8:30

score 48 · Answer 14 · 2020-07-09 19:16:56

48

Views

Studying the nature of roots?

Published on 09 Jul 2020 - 19:16

score 57 · Answer 15 · 2026-03-27 01:00:09

57

Views

Solve the following non-linear system of equations $x = \alpha \log(y/(1-y)), y = \alpha \log(x/(1-x)) - \beta$ in terms of $\alpha, \beta$

Published on 27 Mar 2026 - 1:00

List Question

Using sum-to-product formula to solve $\sin(2\theta)+\sin(4\theta)=0$

Sturm's theorem giving wrong answer for a particular exponential polynomial?

Is there such polynomials that exist?

Is the set of all monic polynomials in $\mathbb{C}[X]$ with roots in a compact set $K$ compact?

Is Po-Shen Loh's trick for roots efficient?

Unable to finish a proof for existence of $n$-th roots

Find all $z$ such that $(z+1)^7 = z^7$. You do not have to put your answer in the simplest rectangular or exponential form.

Is $f(x) = 0 \implies f'(x) > 0$ a sufficient condition for uniqueness of roots for a smooth (non constant) function $f$?

Let $f$ be continuous. If $f(x) = 0 \implies f$ is strictly increasing at $x$, then $f$ has at most one root.

Solution of quadratic equation in matrix notation

Consider the sum $S=\sum\frac{1}{x^2}$ which is over all the positive real solutions of the equation $\frac{\tan{x}}{x}=n$

If $f(x)= (x-a)(x-b)$ for then the minimum number of roots of equation $\pi(f'(x))^2 \cos(\pi(f(x))) + \sin(\pi(f(x)))f''(x) =0$

Finding roots for algebraic equation

Studying the nature of roots?

Solve the following non-linear system of equations $x = \alpha \log(y/(1-y)), y = \alpha \log(x/(1-x)) - \beta$ in terms of $\alpha, \beta$

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