The irrational root theorem says that irrational roots come in pairs. How are things like $x^{2}+\sqrt{2}x=0$ possible?
2026-04-01 14:26:40.1775053600
How is it possible for a quadratic equation to have one rational root and one irrational root?
248 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ROOTS
- How to solve the exponential equation $e^{a+bx}+e^{c+dx}=1$?
- Roots of a complex equation
- Do Irrational Conjugates always come in pairs?
- For $f \in \mathbb{Z}[x]$ , $\deg(\gcd_{\mathbb{Z}_q}(f, x^p - 1)) \geq \deg(\gcd_{\mathbb{Q}}(f, x^p - 1))$
- The Heegner Polynomials
- Roots of a polynomial : finding the sum of the squares of the product of two roots
- Looking for references about a graphical representation of the set of roots of polynomials depending on a parameter
- Approximating the first +ve root of $\tan(\lambda)= \frac{a\lambda+b}{\lambda^2-ab}$, $\lambda\in(0,\pi/2)$
- Find suitable scaling exponent for characteristic polynomial and its largest root
- Form an equation whose roots are $(a-b)^2,(b-c)^2,(c-a)^2.$
Related Questions in QUADRATICS
- Do you have to complete the square before using the quadratic formula?
- Roots of the quadratic eqn
- Questions on positivity of quadratic form with orthogonal constraints
- Conjugate quadratic equations
- Do Irrational Conjugates always come in pairs?
- Quadratic Equations and their roots.
- Solving a quadratic equation with square root constants.
- What would the roots be for this quadratic equation $f(x)=2x^2-6x-8$?
- Polynomial Equation Problem with Complex Roots
- Solve $\sin^{-1}x+\sin^{-1}(1-x)=\cos^{-1}x$ and avoid extra solutions while squaring
Related Questions in RADICALS
- Tan of difference of two angles given as sum of sines and cosines
- Symmetric polynomial written in elementary polynomials
- Interesting inequalities
- Prove that $\frac{1}{\sqrt{ab+a+2}}+ \frac{1}{\sqrt{bc+b+2}}+ \frac{1}{\sqrt{ac+c+2}} \leq \frac{3}{2}$
- Radical of Der(L) where L is a Lie Algebra
- Find local extrema $f(x_1,x_2, \ldots , x_n) = \sqrt{(x_1+x_2+\ldots x_n-a)(a-x_1)(a-x_2)\cdots (a-x_n)}$
- A non-geometrical approach to this surds question
- If $\sqrt{9−8\cos 40^{\circ}} = a +b\sec 40^{\circ}$, then what is $|a+b|$?
- Finding minimum value of $\sqrt{x^2+y^2}$
- Polynomial Equation Problem with Complex Roots
Related Questions in IRRATIONAL-NUMBERS
- Convergence of a rational sequence to a irrational limit
- $\alpha$ is an irrational number. Is $\liminf_{n\rightarrow\infty}n\{ n\alpha\}$ always positive?
- Is this : $\sqrt{3+\sqrt{2+\sqrt{3+\sqrt{2+\sqrt{\cdots}}}}}$ irrational number?
- ls $\sqrt{2}+\sqrt{3}$ the only sum of two irrational which close to $\pi$?
- Find an equation where all 'y' is always irrational for all integer values of x
- Is a irrational number still irrational when we apply some mapping to its decimal representation?
- Density of a real subset $A$ such that $\forall (a,b) \in A^2, \ \sqrt{ab} \in A$
- Proof of irrationality
- Is there an essential difference between Cartwright's and Niven's proofs of the irrationality of $\pi$?
- Where am I making a mistake in showing that countability isn't a thing?
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?
The irrational root theorem is true only if the coefficients are integers.