Question

Showing $\sum_{i=1}^nq_i\sqrt{p_i}+q_0$ is irrational for $q_0,...,q_n\in\mathbb{Q}$, $q_1,...,q_n\not=0$, and $p_i$ distinct prime

score 99 · Answer 1 · 2026-03-28 06:59:45

99

Views

Showing $\sum_{i=1}^nq_i\sqrt{p_i}+q_0$ is irrational for $q_0,...,q_n\in\mathbb{Q}$, $q_1,...,q_n\not=0$, and $p_i$ distinct prime

Published on 28 Mar 2026 - 6:59

score 123 · Answer 2 · 2026-03-27 17:06:19

123

Views

Exactly one root of the quadratic expression is in given interval.

Published on 27 Mar 2026 - 17:06

score 213 · Answer 3 · 2018-10-21 06:24:18

213

Views

find the answer in terms of $a$ and $b$ only ($a, b$ are roots of $\ x^4 + x^3 - 1 = 0$

Published on 21 Oct 2018 - 6:24

score 123 · Answer 4 · 2018-10-22 12:37:05

123

Views

Find the number of distinct real roots of a polynomial

Published on 22 Oct 2018 - 12:37

score 52 · Answer 5 · 2026-03-26 17:47:33

52

Views

Does taking an n-th root of a negative number lead to contradictions?

Published on 26 Mar 2026 - 17:47

score 225 · Answer 6 · 2018-10-23 09:01:26

225

Views

Showing that $2z^4-3z^3+3z^2-z+1=0$ has no Real Roots

Published on 23 Oct 2018 - 9:01

score 1.3k · Answer 7 · 2018-10-23 10:06:41

1.3k

Views

Prove that $2z^4-3z^3+3z^2-z+1=0$ has exactly one complex root in each of the four quadrants.

Published on 23 Oct 2018 - 10:06

score 1k · Answer 8 · 2018-10-23 11:03:24

1k

Views

Finding complex roots of $(z-i)^n-(z+i)^n =0$

Published on 23 Oct 2018 - 11:03

score 4.4k · Answer 9 · 2026-03-26 04:53:02

4.4k

Views

Prove that sum of n-th degree roots of complex number is 0

Published on 26 Mar 2026 - 4:53

score 101 · Answer 10 · 2018-10-23 16:41:17

101

Views

Inequality with roots, a step is not clear!

Published on 23 Oct 2018 - 16:41

score 301 · Answer 11 · 2018-10-23 17:50:24

301

Views

How to prove $x^5 + x^4 + x^3 + x^2 + 1 = 0$ has no rational roots?

Published on 23 Oct 2018 - 17:50

score 175 · Answer 12 · 2026-03-28 08:09:56

175

Views

Does this contour integral actually count the roots of $\zeta(s)$ with imaginary part $<T$?

Published on 28 Mar 2026 - 8:09

score 36 · Answer 13 · 2018-10-24 14:00:41

36

Views

How to show the following equality for twice differentiable function?

Published on 24 Oct 2018 - 14:00

score 53 · Answer 14 · 2026-03-30 08:00:13

53

Views

Calculate $\lim_{a \to 0}\frac{2^n-(2-a)(2-2^2a)(2-3^2a).....(2-n^2a)}{2^na}$

Published on 30 Mar 2026 - 8:00

score 127 · Answer 15 · 2018-10-24 21:24:47

127

Views

Equal absolute values of roots of Quadratic equation

Published on 24 Oct 2018 - 21:24

List Question

Showing $\sum_{i=1}^nq_i\sqrt{p_i}+q_0$ is irrational for $q_0,...,q_n\in\mathbb{Q}$, $q_1,...,q_n\not=0$, and $p_i$ distinct prime

Exactly one root of the quadratic expression is in given interval.

find the answer in terms of $a$ and $b$ only ($a, b$ are roots of $\ x^4 + x^3 - 1 = 0$

Find the number of distinct real roots of a polynomial

Does taking an n-th root of a negative number lead to contradictions?

Showing that $2z^4-3z^3+3z^2-z+1=0$ has no Real Roots

Prove that $2z^4-3z^3+3z^2-z+1=0$ has exactly one complex root in each of the four quadrants.

Finding complex roots of $(z-i)^n-(z+i)^n =0$

Prove that sum of n-th degree roots of complex number is 0

Inequality with roots, a step is not clear!

How to prove $x^5 + x^4 + x^3 + x^2 + 1 = 0$ has no rational roots?

Does this contour integral actually count the roots of $\zeta(s)$ with imaginary part $<T$?

How to show the following equality for twice differentiable function?

Calculate $\lim_{a \to 0}\frac{2^n-(2-a)(2-2^2a)(2-3^2a).....(2-n^2a)}{2^na}$

Equal absolute values of roots of Quadratic equation

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