Question

Equation : $16x^{4}-\alpha x^{3}+(2\alpha+17)x^{2}-\alpha x+16=0$

score 100 · Answer 1 · 2019-10-02 22:28:19

100

Views

Equation : $16x^{4}-\alpha x^{3}+(2\alpha+17)x^{2}-\alpha x+16=0$

Published on 02 Oct 2019 - 22:28

score 72 · Answer 2 · 2026-03-31 21:56:27

72

Views

Problem with a system of equation

Published on 31 Mar 2026 - 21:56

score 56 · Answer 3 · 2019-10-05 13:12:57

56

Views

Can someone help me with proving roots?

Published on 05 Oct 2019 - 13:12

score 53 · Answer 4 · 2026-04-03 05:32:24

53

Views

Number of roots of a separable polynomial over a connected ring does not exceed deg $f$.

Published on 03 Apr 2026 - 5:32

score 87 · Answer 5 · 2026-03-25 14:08:57

87

Views

Asymptotic of the positive root of $x^n-\sum_{k=0}^{n-1} x^k = 0$

Published on 25 Mar 2026 - 14:08

score 106 · Answer 6 · 2019-10-06 19:38:28

106

Views

Elementary Number Theory and Congruences

Published on 06 Oct 2019 - 19:38

score 70 · Answer 7 · 2019-10-07 12:43:50

70

Views

If $a+\frac b2 + \frac c3+\frac d4+\frac e5=0$ , $ a+bx+cx^2+dx^3+ex^4=0$ has at least one real zero.

Published on 07 Oct 2019 - 12:43

score 94 · Answer 8 · 2026-03-29 06:54:52

94

Views

Find prime fields over which a polynomial has roots.

Published on 29 Mar 2026 - 6:54

score 637 · Answer 9 · 2019-10-07 14:57:29

637

Views

Show that $(z+1)^8-z^8=0$ has roots $z=-\frac12$, $z=-\frac12(1\pm i\cot(k\pi/8))$; and follow-up questions

Published on 07 Oct 2019 - 14:57

score 134 · Answer 10 · 2026-04-04 16:56:46

134

Views

How do I calculate the exact number of real roots for a polynomial?

Published on 04 Apr 2026 - 16:56

score 998 · Answer 11 · 2026-03-25 03:07:28

998

Views

show $\frac{z}{(1+z)^2}$ is injective in the unit disk

Published on 25 Mar 2026 - 3:07

score 376 · Answer 12 · 2026-03-30 05:26:48

376

Views

How to find the number of roots of the equation $4\cos(e^x)=2^x+2^{-x}$?

Published on 30 Mar 2026 - 5:26

score 126 · Answer 13 · 2026-03-28 01:35:17

126

Views

Prove that $\sum_{n=0}^\infty\frac{x^{2n+1}}{1+x^{4n+2}}\neq0$ for complex $x$

Published on 28 Mar 2026 - 1:35

score 222 · Answer 14 · 2019-10-11 15:19:47

222

Views

If $x=\sqrt2+\sqrt3+\sqrt6$ is a root of $x^4+ax^3+bx^2+cx+d = 0$ the what is the value of $|a+b+c+d|$?

Published on 11 Oct 2019 - 15:19

score 4.4k · Answer 15 · 2026-04-01 14:59:51

4.4k

Views

Find the polynomial equation of the lowest degree with rational coefficients whose one root is.......?

Published on 01 Apr 2026 - 14:59

List Question

Equation : $16x^{4}-\alpha x^{3}+(2\alpha+17)x^{2}-\alpha x+16=0$

Problem with a system of equation

Can someone help me with proving roots?

Number of roots of a separable polynomial over a connected ring does not exceed deg $f$.

Asymptotic of the positive root of $x^n-\sum_{k=0}^{n-1} x^k = 0$

Elementary Number Theory and Congruences

If $a+\frac b2 + \frac c3+\frac d4+\frac e5=0$ , $ a+bx+cx^2+dx^3+ex^4=0$ has at least one real zero.

Find prime fields over which a polynomial has roots.

Show that $(z+1)^8-z^8=0$ has roots $z=-\frac12$, $z=-\frac12(1\pm i\cot(k\pi/8))$; and follow-up questions

How do I calculate the exact number of real roots for a polynomial?

show $\frac{z}{(1+z)^2}$ is injective in the unit disk

How to find the number of roots of the equation $4\cos(e^x)=2^x+2^{-x}$?

Prove that $\sum_{n=0}^\infty\frac{x^{2n+1}}{1+x^{4n+2}}\neq0$ for complex $x$

If $x=\sqrt2+\sqrt3+\sqrt6$ is a root of $x^4+ax^3+bx^2+cx+d = 0$ the what is the value of $|a+b+c+d|$?

Find the polynomial equation of the lowest degree with rational coefficients whose one root is.......?

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