Question

Sum of Lagrange polynomials: $\sum_{i=0}^{n}L_i(0)x_i^{n+1} = (-1)^{n}x_0\cdot\cdots\cdot x_n $.

score 507 · Answer 1 · 2026-03-25 04:42:35

507

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Sum of Lagrange polynomials: $\sum_{i=0}^{n}L_i(0)x_i^{n+1} = (-1)^{n}x_0\cdot\cdots\cdot x_n $.

Published on 25 Mar 2026 - 4:42

score 342 · Answer 2 · 2026-03-25 06:04:39

342

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How to find integers $p$ and $q$ such that $(p\sqrt{2}+q)^2=34-24\sqrt{2}$

Published on 25 Mar 2026 - 6:04

score 557 · Answer 3 · 2026-03-31 22:28:00

557

Views

Express polynomial as a product of real quadratic polynomials with no real roots

Published on 31 Mar 2026 - 22:28

score 19 · Answer 4 · 2018-09-06 04:41:31

19

Views

Bound Several variables Polynomial $|p(x)|\leq C(1+||x||^2)^N$ for all $x$.

Published on 06 Sep 2018 - 4:41

score 67 · Answer 5 · 2026-04-01 08:06:44

67

Views

Find roots of $x^3-(2\sqrt 2+i)x^2 + (4+2i\sqrt 2)x-4i=0$ knowing that at least one of the roots is from the set $\{i, -i\}.$

Published on 01 Apr 2026 - 8:06

score 287 · Answer 6 · 2026-03-25 08:10:47

287

Views

Show that the projection from $C[0,1]$ onto $P_n[0,1]$ under $L^q$ norm is nonlinear when $q>1$ and $q\neq 2$.

Published on 25 Mar 2026 - 8:10

score 29 · Answer 7 · 2026-04-02 14:08:32

29

Views

Extension field obtained from polynomial

Published on 02 Apr 2026 - 14:08

score 80 · Answer 8 · 2026-03-24 23:55:13

80

Views

Express these polynomials in terms of orthogonal ones

Published on 24 Mar 2026 - 23:55

score 98 · Answer 9 · 2026-04-02 06:59:58

98

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How to find a regular parameter system of the local ring $ \mathbb{C} [X_0, \dots, X_n]_{(P \ )} $?

Published on 02 Apr 2026 - 6:59

score 94 · Answer 10 · 2018-09-06 19:29:37

94

Views

How did Euler derive these complex factors

Published on 06 Sep 2018 - 19:29

score 49 · Answer 11 · 2026-03-27 11:49:59

49

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$S(n)$ the set of all real roots of $p_n(x)$ where $p_{n+1}(x)=p(p_n(x))$, show that $S(n)\subseteq S(2n)$

Published on 27 Mar 2026 - 11:49

score 83 · Answer 12 · 2018-09-07 02:05:45

83

Views

Is it true? $(1+ta_1)(1+ta_2)\cdots(1+ta_n)=1, \;\forall t\in{\Bbb R}$ ⟺ $a_1=a_2=...=a_n=0$

Published on 07 Sep 2018 - 2:05

score 147 · Answer 13 · 2026-03-25 09:33:19

147

Views

Questions about polynomial interpolation problem

Published on 25 Mar 2026 - 9:33

score 118 · Answer 14 · 2026-04-01 09:54:08

118

Views

Find the roots of the polynomial

Published on 01 Apr 2026 - 9:54

score 1k · Answer 15 · 2026-03-25 06:01:55

1k

Views

Finding all three roots of cubic polynomial using Cardano's method

Published on 25 Mar 2026 - 6:01

List Question

Sum of Lagrange polynomials: $\sum_{i=0}^{n}L_i(0)x_i^{n+1} = (-1)^{n}x_0\cdot\cdots\cdot x_n $.

How to find integers $p$ and $q$ such that $(p\sqrt{2}+q)^2=34-24\sqrt{2}$

Express polynomial as a product of real quadratic polynomials with no real roots

Bound Several variables Polynomial $|p(x)|\leq C(1+||x||^2)^N$ for all $x$.

Find roots of $x^3-(2\sqrt 2+i)x^2 + (4+2i\sqrt 2)x-4i=0$ knowing that at least one of the roots is from the set $\{i, -i\}.$

Show that the projection from $C[0,1]$ onto $P_n[0,1]$ under $L^q$ norm is nonlinear when $q>1$ and $q\neq 2$.

Extension field obtained from polynomial

Express these polynomials in terms of orthogonal ones

How to find a regular parameter system of the local ring $ \mathbb{C} [X_0, \dots, X_n]_{(P \ )} $?

How did Euler derive these complex factors

$S(n)$ the set of all real roots of $p_n(x)$ where $p_{n+1}(x)=p(p_n(x))$, show that $S(n)\subseteq S(2n)$

Is it true? $(1+ta_1)(1+ta_2)\cdots(1+ta_n)=1, \;\forall t\in{\Bbb R}$ ⟺ $a_1=a_2=...=a_n=0$

Questions about polynomial interpolation problem

Find the roots of the polynomial

Finding all three roots of cubic polynomial using Cardano's method

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