# Tagged Questions

Questions about the set of values at which a given function evaluates to zero. For questions about "square roots", "cube roots", and such, consider using the (radicals) and (arithmetic) tag. For questions about roots of Lie algebras, use the (lie-algebra) tag instead.

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### how to show whether there are non-real roots in the unit disc of this equation?

For the equation $e^z=e^2z$, $|z|\leq 1$. I have shown there are no roots on the imaginary axis and boundary of the unit disc by simple computing. And let $z=x+iy$ ($x^2+y^2\leq 1$). $e^z=e^2z$ ...
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### Explanation of Chandrupatla's algorithm for root finding?

Is there any writeup of Chandrupatla's algorithm for root finding, besides his original article? A new hybrid quadratic/bisection algorithm for finding the zero of a nonlinear function without using ...
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### What are roots of $x^{3}+3x^{2}+4x+1$?

There are no divisor of 1 in this polynomial for which would be satisfied $x^{3}+3x^{2}+4x+1=0$. How to find roots here?
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### How do I find the poles of this difference equation?

I have an equation: $$y(n) = 0.634x(n) - 0.634x(n-2) + 0.268y(n-2)$$ I completed a $z$ transform and got: $$H(z) = \frac{1-0.268z^{-2}}{0.634 - 0.634z^{-2}}$$ What is the next step to find the ...
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### Keeping a parabola's roots after vertical shift

Suppose f(x) = -x(x - a) + b, where a > 0 and b >= 0. When ...
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### Zeros of Bessel functions

Let $J_\nu(x):=\displaystyle\sum^\infty_{k=0}\frac{(-1)^k(x/2)^{\nu+2k}}{k!~\Gamma(\nu+k+1)}$ denote a Bessel function. When $\nu\geq0$, let $0<j_{\nu,1}<j_{\nu,2}<\cdots$ denote the positive ...
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### polynomial roots and density

Let $f(x)=x^2+2x$ be a quadratic polynomial and $\mathcal{R}_f$ be its range. Denote $\mathcal{A}_{i+1}$ be the set of real numbers that lie in $\mathcal{R}_f$ and come from finding roots of ...
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### Question about solving absolute value equation.

What is the sum of all possible solutions to this equations? $|x+4|^2 -10|x+4|=24$ My attempt: Since $(x+4)^2=|x+4|^2$, so I can ignore the absolute sign of the first term. So we only need to deal ...
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### Checking whether there are real solutions to the polynomial equation $x^4-4x^3+ax^2+bx+1=0$ for certain $a, b$

$x^4-4x^3+ax^2+bx+1=0$ What should $a$ and $b$ be, so that the given equation has four real roots? $(4, -6)$ $(6, -4)$ Not getting any start. Tried Descartes sign rule conditions to ...
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### “Error, (in Student:-calculus1:-roots) Cannot determine if this expression is true or false” [closed]

So I am trying to do the calculation which states: intervalsolve(sin(t) = .7, t = 0 .. 4*PI) but whenever I do it, I get the error which says: ...
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### Solve for complex roots of polynomial

My textbook wants to solve for poles of the following polynomial $$\frac{1}{1+(s/j\Omega_c)^{2N}}$$ A pole will be where \begin{align*} 1+(s/j\Omega_c)^{2N} &= 0 \\ s &= ...