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Solving $x^3-x^2+2=0$

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#algebra-precalculus #polynomials #roots #cubics
1k
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Prove that the polynomial $x^4+3x+3$ is irreducible over the field $\mathbb{Q}[2^{1/3}]$

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#abstract-algebra #polynomials #field-theory #extension-field
77
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Any way to show that $x=2$ is only integer solution of this equation :$x^x-x^2(1-x)^4=0$?

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#polynomials #roots
293
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Proving the lemma $\sqrt2\notin\mathbb{Q}(\sqrt3,\sqrt5)$

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#abstract-algebra #polynomials #field-theory #extension-field #irrational-numbers
131
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Proving expression$\geq 2$, where variables are $x,y,z$

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#inequality #polynomials #fractions #substitution
57
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calculate roots with negative power and two variables

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#polynomials #roots
2.3k
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Finding characteristic polynomial of n x n matrix?

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#linear-algebra #matrices #polynomials #characteristic-functions
125
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Using the Euclidean algorithm, deduce that $\gcd(x^3+2x^2+x +4;x^2+1)=1$

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#polynomials #gcd-and-lcm #euclidean-algorithm
5.6k
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Kernel, Range and Basis of a polynomial linear transformation

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#linear-algebra #polynomials #vector-spaces #linear-transformations #matrix-rank
85
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Polynomial division question with trig and bynomial

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#polynomials #divisibility
148
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Upper bound for residue of a rational function with zeros and poles in the disk

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#complex-analysis #polynomials #residue-calculus #rational-functions #meromorphic-functions
287
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$\zeta_5$ has degree $4$ over $\mathbb{Q}$ and $\zeta_7$ has degree $6$ over $\mathbb{Q}$

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#abstract-algebra #trigonometry #polynomials #field-theory #roots-of-unity
20
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Polynomial behavior beyond some finite region.

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#polynomials
76
Views

Euclidean polynomial division problem

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#polynomials #euclidean-algorithm
329
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Finding complex roots of fourth degree polynomial $z^4 + 8z^3 + 16z^2 + 9$

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#algebra-precalculus #polynomials #complex-numbers

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