# 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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### Express roots in polynomials of equation $x^3+x^2-2x-1=0$

If $\alpha$ is a root of equation $x^3+x^2-2x-1=0$, then find the other two roots in polynomials of $\alpha$, with rational coefficients. I've seen some other examples [1] that other roots were ...
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### Zero of holomorphic function

Let $\Omega \subset \mathbb{C}$ be an open set that contains the unit ball $D$ and let $f \in \mathcal{O}(\Omega)$ a non constant map s.t. $|f(z)| = 1$ for all $z \in \partial D$. Show that $f$ has a ...
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### Please check this perturbation solution of polynomial root and truncation order.

I have a quintic polynomial where the coefficients depends on a parameter $c$, i.e. $$a_0(c)+a_1(c)x+a_2(c)x^2+a_3(c)x^3+a_4(c)x^4+x^5$$ I know that the roots of the polynomial are real and non-...
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### Cubic Depressed Form ! What can we deduce form it?

Cubic depressed form with equation $f(x) = x^3 + px + q$ The question is, when $p$ is positive, will the function have $3$ real roots ? or does it have to have $1$ real and $2$ complex roots? My ...
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### False positives with Descartes rule of signs

Descartes rule of sign can be used to isolate the intervals containing the real roots of a real polynomial. The rule bounds the number of roots from above, that is, it is exact only for intervals ...
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### Square root equation

I have the equation $\sqrt{(7-x)} - \sqrt {(x+13)} = 2$ The square root should be expanded so it is square root of $7-x$ - square root of $x+13 = 2$. When i square both sides i get: $7-x - x-13 = 4$...
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### Finding roots of $4$th degree conjugate reciprocal polynomial

I am developing a computer program and the following polynomial, of which I need to obtain the roots, turned up Ax^4 + Bx^3 + Cx^2 + \overline{B}x + \overline{A}, \quad \text{where } A, B,x \in \...
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### Trigonometric Substitution Method to solve Cubic Equation.

Here are the questions. IN the wiki page, it says p has to be smaller than 0. But they didnt really explain why... Therefore, I assume it is impossible to have a complex number inside arcosine, is ...
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### How to show that a polynomial does not have real roots

How to show generally that a polynomial does not have real roots. Well, for eg lets take the polynomial $x^8-x^7+x^2-x+15$ . Here the power($n=8$) is even so it can have real roots or it might not ...
Given a monic polyomial $P(x)=x^d+r_{d-1}x^{d-1}+\cdots+a_1r+a_0\in\mathbb{R}[x]$ is there a way to manipulate the coefficients of $P$ in an algebraic way such that the new polynomial has exactly as ...