Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [roots]

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 the (arithmetic) tag. For questions about roots of Lie algebras, use the (lie-algebra) tag instead.

Questions regarding values $x$, such that a function $f$ evaluates to zero at $x$. For questions about "square roots", "cube roots" and such, consider using the and the tag. For questions about roots of Lie algebras, use the tag instead.

6663 questions
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is Root a minus number undefined

Assume that we have a function $f$ such that $f(x) = \sqrt x$ Is a domain of $-1$ undefined. I thought it wouldn’t because the answer would be $i\sqrt x$. However, apparently, it is undefined. Can someone explain to me why?
Atilla Çolak
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Bound for the number of roots of an equation

I am trying to find the number of roots (or an upper bound thereof) of a very long transcendental equation. My question is what topic I should study in order to help. I do not need to solve the equation, an upper bound (not infinity please!) for the…
Quadratic Reciprocity
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Finding $341a - a^5$ when $a^2 + 2a - 13 = 0$

Suppose $a$ is a root of $x^2 + 2x - 13.$ Than, find the value of $341a - a^5.$ I was thinking of trying to find a substitution to find the value of $341a - a^5,$ but I'm not sure what. Can someone give me a hint?
questionasker
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How to effciently solve a radical equation of the form $0=\sum_{j=1}^n a_j\sqrt{|b_j-x|}$?

Given a radical equation of the form $$0=\sum_{j=1}^n a_j\sqrt{|b_j-x|}$$ where $b_j>0$ and the sign of $a_j\in\mathbb R$ matches that of $b_j-x$, is there any more efficient (analytical?) solution for $x$ than iteratively putting one square root to…
Tobias Kienzler
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First time with a simple transcendental equation

I need to solve this simple transcendental equation, but I don't exactly know how. $cos(x - 2y) + 8x + 4y = 0$ I mean, I think I've never learnt any method to try solving an equation like this. The only way I can think of is the bisection method,…
Lennard.
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Sign of zeros of $\lambda^2+2\lambda+1-a+\frac{ar}{\delta}=0$ without explicit calculation

I am interested in the zeros of this polynomial in $\lambda$: $$\lambda^2+2\lambda+1-a+\frac{ar}{\delta}=0$$ where $00$. How to determine the sign of their real parts without explicit calculation?
Mark
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Searching simple identities between power sums of roots?

The Newton-Girard identities relating Vieta coefficients $e_k$ with power sums $P_k$ of roots of a polynomial, namely,$$ke_k = \sum_{i = 1}^k (-1)^{i - 1}e_{k-i}P_k$$ {with $e_1$ = $P_1$, and $e_k$ = 0 for $k$ exceeding the degree of polynomial in…
Beedassy Lekraj
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Find al real solutions of $2(2^x- 1) x^2 + (2^{x^2}-2)x = 2^{x+1} -2$

Not sure how to do this. I had a hint to prove that $(2^x- 1)$ and $x$ have the same sign, but how would that help me? Please help!
Cheez
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$ax+bx^{5/3} = c$

in the following equation $$ax+bx^{5/3} = c$$ $a, b$, and $c$ are constant. Through numerical result I know that $x$ is near zero and positive. I want to find an analytical solution or approximation. I really appreciate if you could help me through…
amir
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How to find the amount of irrational roots just based on knowing the amount of rational and real roots in a polynomial?

If i know the amount of of rational roots in a polynomial and the amount of real roots in a polynomial. Can subtract the amount of rational roots in from the amount of Real roots in the polynomial to get the amount of irrational roots in a…
kingmath2999
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Solve for the roots in the following equations

I have two equalities: $$ \alpha x^{2} + \alpha y^{2} - y = 0 $$ $$ \beta x^{2} + \beta y^{2} - x = 0 $$ Where $$ \alpha, \beta $$ are both known constants. How can I solve for $x$ and $y$?
Jad Tawil
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solve $x^2+2ix+1=0$

Hey folks I'm trying to solve $x^2+2ix+1=0$. Squaring it ($x^2+2ix=-1)^2 \implies x^4-4x=1 \implies$ ... leads nowhere Factoring it ($x^2+2ix+1=0)^2 \implies x(x+i)+(x+1)=0 \implies$ ... leads nowhere I know that the answer is $(-1\pm \sqrt2)i$. Any…
user620319
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Finding the "order of a root" at a value

I am given the following problem: The order $p$ of a root $x$ of a function $f$ is the order of the smallest non vanishing derivative at the point $x$. For example, if $f(x) = x^2$, then the order of the root at $x = 0$ is 2. Find the order…
Dean P
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Find real root of cubic equation $(x-1)^3 - (x-1) + 4 = 0$

a) $$(x-1)^3 - (x-1) + 4 = 0$$ When I expanded, I got $$x^3 - 3x^2 + 2x + 4 = 0$$ however I do not know what to do next. b) $$8x^3 - 2x + 4 = 0$$ After I factored, I got $$2(4x^3 - x + 2) = 0$$ however I do not know what to do next.
Lukas 11
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Solving Cubic Roots By Hand

Using a method found here: https://www.wikihow.com/Calculate-Cube-Root-by-Hand, I was able to calculate cubic roots fairly quickly by hand. I did however run into something confusing. Most roots work fine but when I try to calculate the cubic root…
Zachary Heuss
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