Question

A question about polynomials and imaginary roots

score 35 · Answer 1 · 2020-03-31 12:44:52

35

Views

A question about polynomials and imaginary roots

Published on 31 Mar 2020 - 12:44

score 110 · Answer 2 · 2020-04-02 05:09:34

110

Views

A problem regarding the root of a continuously differentiable function on $\mathbb R$

Published on 02 Apr 2020 - 5:09

score 40 · Answer 3 · 2026-04-02 20:11:34

40

Views

Determining how the given number lies in relation to the roots of a quadratic equation

Published on 02 Apr 2026 - 20:11

score 97 · Answer 4 · 2026-03-26 20:44:30

97

Views

Cubic with negative real roots — inequality on coefficients

Published on 26 Mar 2026 - 20:44

score 66 · Answer 5 · 2020-04-03 08:51:56

66

Views

What is the answer to $n$-th root of $n$ as $n$ approach infinity? Is the answer reach 1?

Published on 03 Apr 2020 - 8:51

score 112 · Answer 6 · 2026-03-26 20:41:07

112

Views

If $\ x^3+px-q=0 $ has three roots $a$, $b$, $c$ then find an equation with roots $a+b$, $b+c$ and $c+a$

Published on 26 Mar 2026 - 20:41

score 330 · Answer 7 · 2026-04-02 20:11:02

330

Views

Find all roots of the polynomial equation $p(p(x)) - x = 0$

Published on 02 Apr 2026 - 20:11

score 756 · Answer 8 · 2026-04-02 19:22:27

756

Views

Find the values of $x$ in terms of $a$ in $x^2+\frac{(ax)^2} {(x+a)^2} =3a^2$

Published on 02 Apr 2026 - 19:22

score 262 · Answer 9 · 2026-03-25 03:03:50

262

Views

Showing $1-2z^2-2z^3-2z^4-2z^5$ has a unique root inside the disk of radius 0.6

Published on 25 Mar 2026 - 3:03

score 973 · Answer 10 · 2026-03-31 18:37:45

973

Views

Finding a monic polynomial with integer coefficients having $\sqrt{2} + \sqrt{3} + \sqrt{5} + \sqrt{7}$ as one of its roots.

Published on 31 Mar 2026 - 18:37

score 68 · Answer 11 · 2026-04-01 10:45:49

68

Views

If $\ \frac{a^3+1}{a} = \frac{b^3+1}{b} = \frac{c^3+1}{c} $ find $\ a^3+b^3+c^3 $ if a,b and c are distinct

Published on 01 Apr 2026 - 10:45

score 44 · Answer 12 · 2020-04-05 13:20:54

44

Views

If the equation $(x^2-4)^3(x^3+1)^n(x^2-5x+6)^m=0$ has 18 roots, find m+n.

Published on 05 Apr 2020 - 13:20

score 184 · Answer 13 · 2026-04-08 05:39:12

184

Views

Show that $p(x) = ax^3+bx^2+cx+d$ has no integer roots, where $a,b,c,d\in\mathbb{Z}$ and $p(0), p(1)$ are odd

Published on 08 Apr 2026 - 5:39

score 41 · Answer 14 · 2020-04-05 23:51:06

41

Views

Is there a polynomial $f \in \Bbb C[x_1,...,x_n]$ such that $f(v_i)$ is nonzero for all $i$ and $f(0)=0$?

Published on 05 Apr 2020 - 23:51

score 225 · Answer 15 · 2026-02-23 06:39:36

225

Views

Find the polynomial of integral coefficient with minimum degree and root $z+z^3+z^9$.

Published on 23 Feb 2026 - 6:39

List Question

A question about polynomials and imaginary roots

A problem regarding the root of a continuously differentiable function on $\mathbb R$

Determining how the given number lies in relation to the roots of a quadratic equation

Cubic with negative real roots — inequality on coefficients

What is the answer to $n$-th root of $n$ as $n$ approach infinity? Is the answer reach 1?

If $\ x^3+px-q=0 $ has three roots $a$, $b$, $c$ then find an equation with roots $a+b$, $b+c$ and $c+a$

Find all roots of the polynomial equation $p(p(x)) - x = 0$

Find the values of $x$ in terms of $a$ in $x^2+\frac{(ax)^2} {(x+a)^2} =3a^2$

Showing $1-2z^2-2z^3-2z^4-2z^5$ has a unique root inside the disk of radius 0.6

Finding a monic polynomial with integer coefficients having $\sqrt{2} + \sqrt{3} + \sqrt{5} + \sqrt{7}$ as one of its roots.

If $\ \frac{a^3+1}{a} = \frac{b^3+1}{b} = \frac{c^3+1}{c} $ find $\ a^3+b^3+c^3 $ if a,b and c are distinct

If the equation $(x^2-4)^3(x^3+1)^n(x^2-5x+6)^m=0$ has 18 roots, find m+n.

Show that $p(x) = ax^3+bx^2+cx+d$ has no integer roots, where $a,b,c,d\in\mathbb{Z}$ and $p(0), p(1)$ are odd

Is there a polynomial $f \in \Bbb C[x_1,...,x_n]$ such that $f(v_i)$ is nonzero for all $i$ and $f(0)=0$?

Find the polynomial of integral coefficient with minimum degree and root $z+z^3+z^9$.

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