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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2answers
31 views

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 ...
0
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0answers
10 views

Keeping a parabola's roots after vertical shift

Suppose f(x) = -x(x - a) + b, where a > 0 and b >= 0. When ...
2
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1answer
51 views

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 ...
0
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0answers
17 views

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 ...
0
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1answer
18 views

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 ...
-3
votes
2answers
93 views

In $ \mathbb{Z}[x]$, root $a\in \mathbb{Q}$ $\Rightarrow$ $a\in \mathbb{Z}$ [closed]

Let monic $f(x)\in \mathbb{Z}[x]$. Let $a\in \mathbb{Q}$ where $f(a)=0$. Prove that $a\in \mathbb{Z}$ Thinking the answer below looks alot like the proof of rational root test. Suppose $a \not ...
0
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0answers
25 views

Which is the default Standard Deviation Formula

I have to implement a test from research paper which says: As for testing criteria, standard deviation or min-to-90th percentile ( ) of large packets (1500 B) can be effectively used to find the ...
2
votes
2answers
68 views

proving the existence of a complex root

If $x^5+ax^4+ bx^3+cx^2+dx+e$ where $a,b,c,d,e \in {\bf R}$ and $2a^2< 5b$ then the polynomial has at least one non-real root. We have $-a = x_1 + \dots + x_5$ and $b = x_1 x_2 + x_1 x_3 + ...
0
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1answer
27 views

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 ...
0
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1answer
40 views

“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: ...
0
votes
1answer
15 views

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 &= ...
1
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3answers
37 views

Finding maximum $b$ in $x^5-20x^4+bx^3+cx^2+dx+e=0$

Let $b, c, d, e$ be real numbers such that the following equation $$x^5-20x^4+bx^3+cx^2+dx+e=0$$ has real roots only. Find the largest possibe value of $b$. What I have done is: Let $x_1, x_2, x_3, ...
1
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2answers
51 views

How to solve $c_1x+c_2x^2+…+c_nx^n = K $ type equation (internal rate of return)

I'm trying to calculate internal rate of return and wonder how you would solve this equation $50x + 20 x^2+75x^3 = 135.6$ The answer is $x = 0.9694$ But does anyone know how to do this ...
0
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1answer
39 views

Finding irrational and complex roots of a cubic polynomial

I've got a question which shows short answers and no method so I'm trying to find a hand performed method of solving the cubic polynomial for the roots: ...
3
votes
2answers
44 views

Roots of a quadratic polynomial over a finite field

I am having a hard time figuring this problem out. I have not come up with anything substantial in terms of solving it. Any help would be great. Show that if $z \in F_{p^2}$ is a root of the ...
1
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1answer
58 views

is ${x^{2/3}}$ the same as ${\sqrt[3]{(x^2)}}$ or ${(\sqrt[3]x)^2}$? domain?

is ${x^{2/3}}$ the same as ${\sqrt[3]{x^2}}$ and ${(\sqrt[3]x)^2}$? and what is domain of $x$? Wolfram Alpha shows different results for ${x^{2/3}}$ and ${\sqrt[3]{x^2}}$ representations. Is domain ...
0
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0answers
11 views

Is there any algorithm to find suitable function for fixed-point iteration?

As we know, in the fixed-point method, for finding the root of an equation $f(x) = 0$ in $(a,b)$, we have to rewrite the equation in a way that there is such $g(x)$ which satisfies these conditions: ...
0
votes
1answer
21 views

Root $ c \in F$, where $c\neq0$ $ F[x]$ and div $c^{-1}$

Let $f(x)=a_0+a_1x+...a_{n-1}+a_nx^n $ and $\bar{f}(x)=a_n+a_{n-1}x+...+a_1x^{n-1}+a_0x^n \in F[x]$. ($F$ is a field, of course.) If $c\ne0$ is a zero of $f(x)$, prove $c^{-1}$ is a zero of ...
5
votes
2answers
272 views

Finding roots of equation

$$r\left(\frac 1p -1\right)- \left(\frac 1p\right)^\frac89 + \left(\frac 1p\right)^\frac19 =0$$ where $ r = 2^\frac89 - 2^\frac19$ How do I solve this without a computer?
1
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3answers
138 views

What is the purpose of finding roots?

I think I know what a root is. It's the value of elements in the domain of a function that map to 0 in the range of the function. At least that's how I see it. Do correct me if I'm wrong. However I ...
0
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1answer
14 views

roots of bivariate polynomial over prime field

We know any polynomial with degree n over real field has at most n roots. Let $p(x)$ is a bivariate polynomial with degree $n$ over prime field $F_p$. How many roots existe over $F_p$ ? If $p(x)$ be a ...
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0answers
82 views

Solving Cardano Triplets

Reading https://projecteuler.net/problem=251 I'm attempting to solve the example provided : $ 3 \sqrt {a + b \sqrt c} $ + $ 3 \sqrt {a - b \sqrt c} $ = 1 a=2 b=1 c=5 $ 3\sqrt {2+(1)\sqrt5} + ...
0
votes
1answer
33 views

General formula for special Polynomial

is there a special formula to find the roots of a polynomial like $$P(x) = x^{b+c} + \alpha x^b + \beta x^c -\gamma = 0$$
1
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1answer
35 views

Methods for find common roots of two functions

Are there any methods for finding the common roots of two functions? I would like to know if such a method exists, which doesn't involve finding all the roots of both functions. While I'd like to ...
0
votes
1answer
66 views

How to find solutions for four polynomial equations with four unknown variables using RESULTANT THEORY?

Can I use resultant theory (or polynomial resultant method) to find solutions for FOUR simultaneous polynomial equations with FOUR unknown variables? So far, I could only find examples which uses TWO ...
0
votes
3answers
31 views

Getting the roots of higher degree polynomial [closed]

So I need to get the roots of this polynomial $x^4 - 16x^2 + 100 = 0$. Hours of trying to solve for the answer led me to the easiest way of getting these said roots: wolfram alpha. It gave me $-3 \pm ...
0
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2answers
58 views

Algorithm for finding all roots of linear Diophantine equation with finite solution space

I have the following Diophantine equation: $$17a_1+16a_2+\dots+2a_{16}+a_{17}+c=0$$ with $c$ being a constant integer value, where I have two concrete cases: $c=-200$ and $c=-40$. I am looking for ...
1
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2answers
86 views

Find root of $x\cdot 2^x - 1$ function

Is it possible to solve the equation: $x2^x - 1 = 0$ without using the function graph? According to the function plot, its root is around 0.6. I need to get the numeric value of the function's ...
0
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1answer
30 views

Determine how many roots of special n-degree polynomial are positive integers [closed]

I have a special polynomial of the form $x^n + bx + c = 0$ $c = b - 1$ How can I determine how many of the possible values of $x$ are positive integers? All values of $n$ will be positive integers.
2
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1answer
33 views

Unique solution of algebraic equation

Prove that $10^x+11^x+12^x=13^x+14^x$ has an unique solution over $\mathbb R$. By inspection the equation is true for $x=2$
1
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1answer
36 views

Find an equation of the quadratic function with zeros at $(0, 0)$ and $(6, 0)$ with $f(5) = -15$

The Question is: write the equation of the quadratic function with zeros at $(0,0)$ and $(6,0)$ with $f(5) = -15$. So, I know how to get the equation from the zeros, but I am confused with what I am ...
0
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1answer
103 views

Find all roots of a polynomial using secant method [closed]

I am writing a program that will find all zeros of a polynomial using secant method. But this method despite my best efforts doesn't always converge. How to find the initial value for the secant ...
2
votes
1answer
36 views

Finding the number of a roots in an equation modulo n

I am looking for some n such that $$x^2+x=0\pmod{n}$$ has at least 4 solutions. Is there any way of doing this reasonably quickly without having to check every solution manually? There must be. ...
1
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0answers
64 views

What is the highest degree this polynomial can have?

Let P be a polynomial and its coeficiants are 1 or -1. and all roots are real number. What is the highest degree this polynomial can have? By the integer root theorem. $\pm1$ maybe a root. I think ...
-1
votes
2answers
27 views

how to calculate compound interest when year is not whole?

The formula for compound interest is Annual Compound Interest Formula: $$A = P\left(1+\frac{r}{n}\right)^{nt}$$ Here year is a whole number. So how can I calculate compound interest on 40,000 for ...
0
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0answers
50 views

asymptotic solutions [duplicate]

Currently taking a new module and although I am understanding the lectures - I am finding it difficult to translate this into exercises so I am looking for help. Hopefully I am just missing something ...
17
votes
7answers
2k views

Find all five solutions of the equation $z^5+z^4+z^3+z^2+z+1 = 0$

$z^5+z^4+z^3+z^2+z+1 = 0$ I can't figure this out can someone offer any suggestions? Factoring it into $(z+1)(z^4+z^2+1)$ didn't do anything but show -1 is one solution. I solved for all roots of ...
0
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3answers
77 views

Show that there exists a root of the equation

Show that there exists a root of the equation $ x^2-x-1= \frac{1}{x+1} $ I don't know where to start. I need hints.
2
votes
0answers
43 views

Number of “possible” rational roots of a univariate polynomial

Is it possible to determine the number of possible rational roots of a single variable polynomial? polynomial a0 + a1x + a2x^2 + ... + anx^n. This is to find ...
1
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1answer
44 views

If a cubic has three real roots, must its factor quadratic equation have real roots too?

The question I'm trying to answer is for what values of $p$ does $f(x)=x^3 + px^2 + qx - 4$ have three real roots. It is given that $(x-1)$ is a factor of $f(x)$ and that $p + q = 3$. Using algebraic ...
7
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1answer
122 views

How to choose the right branch to find the roots.

I want to find the roots of $$f(z)=\left[a+zg(z)\right]^2+g(z)^2=0$$ Where $a$ is real number and: $$ g(z)=\frac{1}{2\sqrt{z^2+1}}\ln\left(\frac{z+\sqrt{z^2+1}}{z-\sqrt{z^2+1}}\right) $$ It is ...
2
votes
1answer
46 views

Nulls are located at all primes on the real axis?

This page claims "a complex function, whose nulls are located at all primes on the real axis" $$f(z) = \left| 2 - \sum\limits^\infty_{k=1} \frac{1}{k} \frac{e^{2 \pi i z}-1}{ e^{2 \pi i z / k}-1} ...
1
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2answers
75 views

How to solve $e^x=kx + 1$ when $k > 1$?

It's obvious that $x=0$ is one of the roots. According to the graphs of $e^x$ and $kx + 1$, there's another root $x_1 > 0$ when $k > 1$. Is there a way to represent it numerically.
1
vote
1answer
76 views

oscillation of newton iteration for arctan

We consider the function f(x) = arctan(x), we know that the newton iteration might diverge for some starting value too far from the zero. But it might also lead to an oscillation between two values as ...
0
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0answers
26 views

What's the flaw in this derivation? Obtaining the condition that $f(z)=0$ have real values.

I want to find the condition for equation $$f(z)=\left[a+zg(z)\right]^2+g(z)^2=0$$ to have real roots, where $a$ is real number and: $$ ...
4
votes
0answers
51 views

Symmetric proof for the probability of real roots of a quadratic with exponentially distributed parameters

What is the probability that the polynomial has real roots? asked for the probability that the quadratic polynomial $ax^2+bx+c$ has real roots if the parameters $a,b,c$ are exponentially distributed ...
0
votes
1answer
18 views

find the solution set of the following equation with absolute value

WA online me results $x = -5$, failed to reach it $$\left ( \left | x \right |+2 \right )\left ( \left| x-2 \right| -3\right)=x^{2}+3$$
0
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1answer
27 views

Prove that $z^5+(4/3)e^z \sin z-16iz+48$ has five zeroes in the disk $|z|<3$

Prove that $z^5+(4/3)e^z \sin z-16iz+48$ has five zeroes in the disk $|z|<3$ I could prove it using Rouche's theorem if it werent for the second term. For other three terms, the modulus on the ...
0
votes
1answer
48 views

What is the fastest technique to find complex roots of a function?

I have the following function: $$ay^6+by^3+c=0$$ It can be re-written in the quadratic form: $$ax^2+bx+c=0$$ In my case, $a=1, b=-7, c=-8$; then the quadratic equation equals $(x-8)(x+1)$, therefore, ...
0
votes
0answers
38 views

Can one have an infinity multiplicity of zeroes for a function?

With a function $f(z)=e^z -1, \, z_0 =2k \pi i, \, k \in \mathbb{Z}$. The multiplicity should be $k$. But could one say that we have an infinite multiplicity zero at $z_0$ if $k \to \infty$?