List questions from roots

Published on 29 Mar 2026 - 19:07

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Solve $3x(2+\sqrt{9x^2 + 3}) + (4x-2)(\sqrt{x^2 - x +1}+1) = 0$ for $x\in \mathbb{R}$

Published on 05 Jul 2019 - 18:34

147

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Roots of $(x-\lfloor x\rfloor)^2+(x-\lfloor x\rfloor)\left\lfloor{1\over x -\lfloor x\rfloor}\right\rfloor=1$

Published on 26 Mar 2026 - 14:22

7.4k

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Roots of quadratic equation $ax^2+bx+c$ at infinity

Published on 27 Mar 2026 - 0:04

66

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Prove that $f(x)=2x-L\cos(Lx)$ has only one root in range $x\in [-1, 1]$ when $L \in [0, \pi/2]$

Published on 07 Jul 2019 - 10:31

292

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Roots of $z^4 + 2z^3 + 20z + 12 = 0$

Published on 07 Jul 2019 - 18:26

120

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Compute the derivative analytically of an equation that has no closed-form solution

Published on 25 Mar 2026 - 21:49

77

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Finding root of an equation

Published on 27 Mar 2026 - 8:16

628

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Inverting a monotone polynomial

Published on 26 Mar 2026 - 9:45

104

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How to find the double roots of $f(x) = x^6 -x^4 +x^2 - 1$

Published on 09 Jul 2019 - 12:32

513

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Why does this quadratic expression have three zeroes?

Published on 29 Mar 2026 - 23:41

135

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Asymptotic growth of solutions to $x - C \log x = 0$

Published on 02 Apr 2026 - 17:10

49

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Don't understand why this quadratic form can vanish only two times on the arc [-π/2, π/2]

Published on 26 Mar 2026 - 17:34

491

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Find a new cubic equation with new roots $\alpha\beta$, $\beta\gamma$ and $\gamma\alpha$. Can I use substitution for this?

Published on 25 Mar 2026 - 20:11

65

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finding roots of an equation

Published on 25 Mar 2026 - 21:48

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Calculating complex roots

Solve $3x(2+\sqrt{9x^2 + 3}) + (4x-2)(\sqrt{x^2 - x +1}+1) = 0$ for $x\in \mathbb{R}$

Roots of $(x-\lfloor x\rfloor)^2+(x-\lfloor x\rfloor)\left\lfloor{1\over x -\lfloor x\rfloor}\right\rfloor=1$

Roots of quadratic equation $ax^2+bx+c$ at infinity

Prove that $f(x)=2x-L\cos(Lx)$ has only one root in range $x\in [-1, 1]$ when $L \in [0, \pi/2]$

Roots of $z^4 + 2z^3 + 20z + 12 = 0$

Compute the derivative analytically of an equation that has no closed-form solution

Finding root of an equation

Inverting a monotone polynomial

How to find the double roots of $f(x) = x^6 -x^4 +x^2 - 1$

Why does this quadratic expression have three zeroes?

Asymptotic growth of solutions to $x - C \log x = 0$

Don't understand why this quadratic form can vanish only two times on the arc [-π/2, π/2]

Find a new cubic equation with new roots $\alpha\beta$, $\beta\gamma$ and $\gamma\alpha$. Can I use substitution for this?

finding roots of an equation

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