Let $\alpha \in \mathbb{C}$ be a root of polynomial $z^3+z+3$
How can I find a minimal polynomial of $\alpha - \alpha^2$ over $\mathbb{Q}$?
2026-04-03 16:31:48.1775233908
Find a minimal polynomial of element
51 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in NUMBER-THEORY
- Maximum number of guaranteed coins to get in a "30 coins in 3 boxes" puzzle
- Interesting number theoretical game
- Show that $(x,y,z)$ is a primitive Pythagorean triple then either $x$ or $y$ is divisible by $3$.
- About polynomial value being perfect power.
- Name of Theorem for Coloring of $\{1, \dots, n\}$
- Reciprocal-totient function, in term of the totient function?
- What is the smallest integer $N>2$, such that $x^5+y^5 = N$ has a rational solution?
- Integer from base 10 to base 2
- How do I show that any natural number of this expression is a natural linear combination?
- Counting the number of solutions of the congruence $x^k\equiv h$ (mod q)
Related Questions in EXTENSION-FIELD
- Field $\mathbb{Q}(\alpha)$ with $\alpha=\sqrt[3]7+2i$
- $\overline{A}\simeq\overline{k}^n $ implies $A\simeq K_1\times\cdots\times K_r$
- Extension of field, $\Bbb{R}(i \pi) = \Bbb{C} $
- A field extension of degree $\leq 2$
- Field not separable
- Intersections of two primitive field extensions of $\mathbb{Q}$
- Fields generated by elements
- Find the degree of splitting field of a separable polynomial over finite field
- Eigenvalues of an element in a field extension
- When a product of two primitive elements is also primitive?
Related Questions in MINIMAL-POLYNOMIALS
- Minimal polynomial of $f(A) = A^t$
- Minimal polynomial of $ab$, when those of $a$ and $b$ are known
- Finding the minimal polynomial of $uv$, when those of $u$ and $v$ are given and of degree three
- Jordan chevaley decomposition and cyclic vectors
- A field extension of degree $\leq 2$
- For a non diagnolizable Matrix $A_{n\times n}$ exists a non zero polynomial $p(t)$ of degree $< n$ s.t. $(p(A))^2=0$
- minimal polynomial, $E_p=\cos\frac{2\pi}{p} + i\sin\frac{2\pi}{p}$
- Minimal polynomial of $\sqrt{3}$ over $\Bbb{Q}(\sqrt[6]{3})$
- Irreducibility of $f(x)=x^4+4x-1$
- Jordan forms associated with characteristic polynomials and minimal polynomials
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
One way to do this is to set $y=z-z^2$ and eliminate $z$ using $z^3+z+3=0$.
Note: The first equation enables you to reduce the second to an expression linear in $z$. Then express $z$ in terms of $y$ and feed into the first equation.