Question

Number of real roots of polynomial equation $\sum_{j=1}^n \frac{a_j}{(\lambda_j+x )^2}=1$

score 60 · Answer 1 · 2026-04-16 14:08:03

60

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Number of real roots of polynomial equation $\sum_{j=1}^n \frac{a_j}{(\lambda_j+x )^2}=1$

Published on 16 Apr 2026 - 14:08

score 73 · Answer 2 · 2026-04-16 12:02:51

73

Views

Prove that in $a_1 x^{n_1} + a_2 x^{n_2} + \dots + a_k x^{n_k}$, $n_1 < n_2 < \dots < n_k$, each non-zero root has multiplicity not above $k-1$

Published on 16 Apr 2026 - 12:02

score 31 · Answer 3 · 2026-04-11 00:26:21

31

Views

Are zeros of a cubic polynomial lipschitz wrt the constant term?

Published on 11 Apr 2026 - 0:26

score 45 · Answer 4 · 2026-04-17 15:28:49

45

Views

What is the sum of all the roots of the equation $x|x|-5|x+2|+6=0$?

Published on 17 Apr 2026 - 15:28

score 25 · Answer 5 · 2026-04-16 15:45:12

25

Views

Order of zeros of $2(z-1)^n-e^{-z}$ in $B_1(1)$.

Published on 16 Apr 2026 - 15:45

score 52 · Answer 6 · 2026-04-09 11:54:32

52

Views

Interval Newton Method - not converging

Published on 09 Apr 2026 - 11:54

score 29 · Answer 7 · 2026-04-16 13:45:11

29

Views

Ensure convergence of a sequence of thresholds

Published on 16 Apr 2026 - 13:45

score 26 · Answer 8 · 2026-04-11 05:47:20

26

Views

complex zeros of difference of $n$th powers of affine polynomials

Published on 11 Apr 2026 - 5:47

score 78 · Answer 9 · 2026-04-15 23:09:33

78

Views

Solutions of $x^2+x(a+b+c)+\lambda(ab+ bc+ac)$ are real

Published on 15 Apr 2026 - 23:09

score 39 · Answer 10 · 2026-04-13 18:25:19

39

Views

What is Hurwitz Theorem and how is it applied?

Published on 13 Apr 2026 - 18:25

score 26 · Answer 11 · 2026-04-13 01:30:47

26

Views

Roots of sums of functions

Published on 13 Apr 2026 - 1:30

score 74 · Answer 12 · 2026-04-10 08:28:34

74

Views

Finding closed-form maximum of a function with no obvious root

Published on 10 Apr 2026 - 8:28

score 53 · Answer 13 · 2026-04-11 21:39:06

53

Views

find if there exists a zero of a function that's defined by an integral

Published on 11 Apr 2026 - 21:39

score 42 · Answer 14 · 2026-03-25 18:07:49

42

Views

How to lead a shot at a target undergoing uniform circular motion

Published on 25 Mar 2026 - 18:07

score 89 · Answer 15 · 2026-04-08 16:13:43

89

Views

Confusion about matrix polynomials

Published on 08 Apr 2026 - 16:13

List Question

Number of real roots of polynomial equation $\sum_{j=1}^n \frac{a_j}{(\lambda_j+x )^2}=1$

Prove that in $a_1 x^{n_1} + a_2 x^{n_2} + \dots + a_k x^{n_k}$, $n_1 < n_2 < \dots < n_k$, each non-zero root has multiplicity not above $k-1$

Are zeros of a cubic polynomial lipschitz wrt the constant term?

What is the sum of all the roots of the equation $x|x|-5|x+2|+6=0$?

Order of zeros of $2(z-1)^n-e^{-z}$ in $B_1(1)$.

Interval Newton Method - not converging

Ensure convergence of a sequence of thresholds

complex zeros of difference of $n$th powers of affine polynomials

Solutions of $x^2+x(a+b+c)+\lambda(ab+ bc+ac)$ are real

What is Hurwitz Theorem and how is it applied?

Roots of sums of functions

Finding closed-form maximum of a function with no obvious root

find if there exists a zero of a function that's defined by an integral

How to lead a shot at a target undergoing uniform circular motion

Confusion about matrix polynomials

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